Year of entry: 2018
Course unit details:
Mathematical Economics II
|Unit level||Level 3|
|Teaching period(s)||Full year|
|Available as a free choice unit?||Yes|
See course Blackboard pages.
|Unit title||Unit code||Requirement type||Description|
|Mathematical Economics I||ECON20120||Pre-Requisite||Compulsory|
The aim of this course is to introduce various mathematical techniques useful in economic analysis and to illustrate their use in economic models.
By the end of this course, students will be able to:
- Use elementary methods to study systems of differential equations.
- Formulate and solve simple economic models, stemming from “real world examples”, in terms of continuous time dynamic programming.
- Solve constrained optimization (static and dynamic) problems.
- Examine stability properties of solutions to economic problems in a dynamic context.
- Demonstrate the understanding of the main solution concepts in game theory.
- Formalize real world situations in terms of either optimization problems or games.
The main focus of the 1st semester is on differential economies and related matters. Central topics include:
- Differential equations with economic applications.
Continuous time dynamic optimization with economic applications.
The focus of the 2nd semester part of the course is modern game theory in the context of mathematical economics. Topics include:
- Simultaneous move games and dynamic games with perfect information. Nash equilibrium and subgame perfect Nash equilibrium. Games with communication. Contracts, implementable allocations and correlated equilibria. The economic models of Cournot, Stackelberg, Bertrand, Hotelling, Bertrand-Edgeworth, the "Monopoly Union" model, and Rubinstein's bargaining model.
- Two stage games with imperfect information and repeated games. Economic models of bank runs. Tariffs and imperfect competition. Infinitely repeated games. The Folk Theorem.
- Incomplete information. Static Bayesian games. Bayesian Nash equilibrium. Cournot and Bertrand models with asymmetric information. Models of auctions. Dynamic Bayesian games. Perfect Bayesian Nash equilibrium. Signalling models.
- Learning and evolutionary models. Fictitious play. Evolutionary stable strategies. Replicator dynamics. Evolutionary stable steady states.
Teaching and learning methods
Semester 1: Lectures and exercise classes.
Semester 2: Lectures, exercise classes and tutorials.
- Analytical skills
- Synthesis and analysis of data and information. Critical reflection and evaluation.
- Problem solving
- Planning independent research using library, electronic and online resources.
- Economic modelling. Presentation. Numeracy. Literacy. Computer literacy. Time management. Applying subject knowledge. Improving own learning.
- Initial Online Assignment - for revision of pre-requisite material. Pass (1) or Fail (0) mark.
- 3 Online Assignments.
- Final Assignments Mark = average of best 2 out of 3 X Mark for initial assignment.
- Final Exam - short written answers.
- Semester mark = Max(Exam, 0.8*Exam+0.2*Assignments).
- Two Take-Home Tests - 10% (out of the total 50%).
- Final Exam - 40% (out of the total 50%).
- Date: May/June examination period
- Length: 1.5 hours
- Structure: three questions in Section A (60 marks); one out of three questions in Section B (40 marks).
- Mock Exam – the exam will be solved by the students in class in one of the further support hours, with supervision and assistance from the lecturer.
- Tutorial feedback.
- Office hours.
- Revision sessions.
- Discussion boards.
Students can get feedback and revision support at small-group tutorial meetings and weekly office hours.
- K. Sydsaeter et al, “Essential Mathematics for Economic Analysis” (FT Press, 2008).
- K. Sydsaeter et al, “Further Mathematics for Economic Analysis” (FT Press, 2008).
- A. C. Chiang and K. Wainwright, “Fundamental Methods of Mathematical Economics” (McGraw-Hill, 2005).
- R. Gibbons, A Primer in Game Theory, 1992.
- M. Maschler, E. Solan, and S. Zamir, Game Theory, 2013.
- This reading is supplementary to the lectures and is optional. The course is self-contained, and no external texts or resources are required to fulfill its objectives. Electronic pdf copies of all course materials (lecture notes/slides, exercises and answers) will be posted to the web during the semester. They are recommended, and fully sufficient, for revising the course and preparing the examination.
|Scheduled activity hours|
|Assessment written exam||3|
|Practical classes & workshops||9|
|Independent study hours|
|Igor Evstigneev||Unit coordinator|
|Omer Idan||Unit coordinator|