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School of Social Sciences

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BAEcon Economics
Learn how the social sciences can help you to understand today's world.

BAEcon Economics / Course details

Year of entry: 2018

Course unit details:
Mathematical Economics I

Unit code ECON30320
Credit rating 20
Unit level Level 3
Teaching period(s) Full year
Offered by Economics
Available as a free choice unit? Yes

Overview

See course Blackboard pages.

Pre/co-requisites

Unit title Unit code Requirement type Description
Further Mathematics ECON20281 Pre-Requisite Compulsory
Pre-requisites: (ECON20281) - maths only, no stats.

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:

  1. Apply the Lagrange and Kuhn-Tucker methods to solve economic optimization problems.
  2. Apply duality theory to construct expenditure and demand functions.
  3. Understand and apply methods of comparative statics.
  4. Solve simple games, including duopoly games.
  5. Solve economic models involving first order one-dimensional and two-dimensional difference equations as well as first order one and two-dimensional 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, first-order conditions, maximum, minimum, second-order conditions.
  • Optimisation under constraints: Equality constraints, inequality constraints, Lagrangian, Kuhn-Tucker-Lagrangian.
  • 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.

 

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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. Decision-making.
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:

  • Mid-Term 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. 

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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 Schenk-Hoppe Unit coordinator

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