BAEcon Economics
Year of entry: 2018
Course unit details:
Mathematical Economics I
Unit code  ECON20120 

Credit rating  20 
Unit level  Level 2 
Teaching period(s)  Full year 
Offered by  Economics 
Available as a free choice unit?  Yes 
Overview
See course Blackboard pages.
Pre/corequisites
Unit title  Unit code  Requirement type  Description 

Advanced Mathematics  ECON10071  PreRequisite  Compulsory 
Introduction to Mathematical Economics  ECON10192  PreRequisite  Compulsory 
ECON10001  PreRequisite  Compulsory 
Aims
The aim of this course is to develop students’ knowledge of the analytical and mathematical techniques used in static and dynamic economic theory.
Learning outcomes
At the end of this course students should be able to:
 Apply the Lagrange and KuhnTucker methods to solve economic optimization problems.
 Apply duality theory to construct expenditure and demand functions.
 Understand and apply methods of comparative statics.
 Solve simple games, including duopoly games.
 Solve economic models involving first order onedimensional and twodimensional difference equations as well as first order one and twodimensional differential equations.
Syllabus
Semester 1:
 Introduction: What is Mathematical Economics about? Learning goals.
 Preferences: Definition, completeness, transitivity, examples.
 Utility functions: From preferences to utility functions.
 Lexicographic preferences.
 Rational choice.
 Consumer: Consumption choice, sets and functions.
 Derivatives: Partial derivative, directional derivative, total derivative, Jacobian matrix, Hessian matrix, examples.
 Optimisation: Extrema of a function, firstorder conditions, maximum, minimum, secondorder conditions.
 Optimisation under constraints: Equality constraints, inequality constraints, Lagrangian, KuhnTuckerLagrangian.
 Concavity and convexity: Sets and functions, applications in optimisation.
 Value functions.
 Envelope Theorem.
 Implicit Function Theorem and its Applications.
 Duality: Walrasian/Marshallian demand, Roy's identity. Sheppard's lemma.
 Summary and review.

Semester 2:
IA Game Theory (Static Games):
 Definition of games, games in normal and strategic forms.
 Solution concepts, best responses, Nash equilibrium with pure strategies.
 Mixed strategies, Nash equilibrium with mixed strategies, existence of Nash equilibrium.
 Applications in economics, Cournot and Bertrand duopoly/oligopoly as a game.
IB Game Theory (Dynamic Games):
 Game trees, games in extensive form, sequential move, multistage and repeated games.
 Solution concepts for dynamic games, subgames, subgame perfection, refinements of Nash equilibrium, subgame perfect Nash equilibrium.
 Applications in economics, duopoly/oligopoly with sequential moves, Stackelberg duopoly, investment/capacity decisions and other examples from industrial organization.
IIA Dynamic Systems (Discrete Time):
 First order linear difference equations, steady state, stability and solutions.
 Applications in economics, market stability.
 First order linear systems of difference equations, steady state, stability and solutions.
 Cyclicality of solutions.
 Applications in economics, the linear first order macroeconomic model, Samuelson's accelerator model, dynamic Cournot duopoly.
IIB Dynamic Systems (Continuous Time):
 First order linear differential equations, steady state, stability and solutions.
 Applications in economics, the Philips curve.
 First order linear systems of differential equations, steady state, stability and solutions.
 Cyclicality of solutions.
 Applications in economics, dynamic Cournot duopoly in continuous time, continuous time macroeconomic model.
Teaching and learning methods
Lectures and tutorial classes.
Employability skills
 Analytical skills
 Critical reflection and evaluation. Decisionmaking.
 Problem solving
 Ability to conduct rigorous analysis of problems.
 Research
 Planning, conducting and reporting on independent research.
 Other
 Mapping and modelling. Peer review. Applying subject knowledge.
Assessment methods
Semester 1:
 Online tests (5 x 6% = 30%).
 Final Exam  part A multiple choice, part B longer questions with choice (70%).
Semester 2:
 MidTerm Exam  multiple choice questions (20%).

Final Exam  part A multiple choice questions, part B 1/2 longer questions (80%).
Feedback methods
Semester 1:
 Tutorial exercises.
 Online tests.
Semester 2:
 Tutorial exercises.
 Further exercises online.
Students can also receive further feedback from tutorials, office hours, revision sessions, discussion boards etc.
Recommended reading
Semester 1:
Reading: Detailed lecture notes are on Blackboard. Please read the relevant chapter BEFORE each lecture.
Reading list: The following textbooks are useful references for the material covered during the semester:
 Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995.
 Jehle, J., and P. Reny, Advanced Microeconomic Theory, Addison Wesley, 2nd ed., 2000.
 Nicholson, W., Microeconomic Theory, 9th ed., 2005.

Rubinstein, A, Lecture Notes in Microeconomic Theory, Princeton University Press, 2nd ed., 2002.
Prerequisite: The students are expected to have a good knowledge of calculus. Among required topics: partial derivatives, the chain rule in several variables, static optimization, etc. Those who feel insecure with the above material (although this is taught in the prerequisite maths modules) should revise it before taking the module. The book of Hammond and Sydsæter “essential mathematics for economic analysis” as well as the advance mathematics unit textbook may serve as good references. Students are expected to revise the mentioned material before semester 1 starts.
Weekly preparation: (1) Read the handout, (2) solve the exercise questions, (3) read the textbook as instructed in the handouts.

Semester 2:
Sets of notes along with exercise sets will be made available on the course website. Further suggested readings are mentioned within those notes. Answers to exercises will be covered during example classes (but WILL NOT be made available by the lecturer). A useful reference for some of the material that will be covered is:
 Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995.

Hal R. Varian, Intermediate Microeconomics a Modern Approach, 8th edition, Norton 2010.
Study hours
Scheduled activity hours  

Assessment written exam  3 
Lectures  32 
Tutorials  20 
Independent study hours  

Independent study  145 
Teaching staff
Staff member  Role 

Leonidas Koutsougeras  Unit coordinator 
Klaus SchenkHoppe  Unit coordinator 