BA Modern Language and Business & Management (French) / Course details

Year of entry: 2022

Course unit details:Mathematical Economics I

Unit code ECON30320 20 Level 3 Full year Economics Yes

Overview

Economics has made a huge jump forward when it became a more formal science. In particular when economics started to formulate its models using mathematics and to use mathematical tools to solve these models.

This is what the course is about: Mathematical Modelling and Analysis. Both of which constitute core skills of economists. The course unit develops students’ knowledge of mathematical and quantitative methods in the context of consumer theory, the theory of the firm, game theory and other subjects.

You will learn how to express an economic idea in mathematical terms. In addition you will learn mathematical methods how to find equilibria, and how to analyse the behaviour of equilibria when exogenous circumstances change. The techniques you will learn on this course are used in almost all branches of economics. The course content is really a universal (mathematical) toolbox for economic modelling.

Although we will look into economic applications, this course is not about learning new economics. You will further your knowledge of economics in the micro, macro, development, etc. economics courses.

The objectives of this course are that students will be able 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 one-dimensional and two-dimensional difference equations
• solve economic models involving first order one and two-dimensional differential equations.

Pre/co-requisites

Unit title Unit code Requirement type Description
Introduction to Mathematical Economics ECON20192 Pre-Requisite Compulsory
Pre-requisites: "ECON20071 and ECON20192"

ECON20071 Adv Maths and ECON20192 Intro Math Econ

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:

• 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 one-dimensional and two-dimensional difference equations
• solve economic models involving first order one and two-dimensional differential equations.

Syllabus

Semester 1:

• What s Mathematical Economics about? Learning goals
• Preferences and utility
• Uncertainty and lotteries
• Review of (constrained) optimisation
• Incentives and their applications
• Mathematical financial economics
• Implicit Function Theorem and its applications in micro and macroeconomics
• Demand theory
• Summary and review

Semester 2:
This part of the course covers Game Theory and Dynamic Systems.
I Game Theory
IA 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 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

II Dynamic systems
IIA 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 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

Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study

Intellectual skills

Critical thinking, Problem solving, Problem posing, conducting and reporting on research, Critical reflection and evaluation, decision-Making.

Practical skills

Ability to conduct rigorous analysis of problems, Planning independent research, Mapping and modelling, Peer review.

Transferable skills and personal qualities

• Applying Subject Knowledge
• Developing Research Proposals
• Developing sophisticated reports with structured arguments

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

Smester One

35% Exam

15% Online test (five, worth 3% each)

Semester Two

40% Exam

10% Mid-term test

Feedback methods

• Tutorial exercises.
• Online tests.

Semester 1:

Reading: Detailed lecture notes are available on Blackboard (one chapter for each hour of lecture). 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
• Sydsæter, K., Hammond, P., Seierstad, A. and Strom, A., Further Mathematics for Economic Analysis, Prentice Hall (now in its second edition).
• Sydsæter, K., Hammond, P., and Strom, A., Essential Mathematics for Economic Analysis, Prentice Hall (now in its fourth edition)
• Simon, C.P. and Blume, L.E., Mathematics for Economists, W.W. Norton (paperback and hard cover)
• 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.

Teaching staff

Staff member Role
Leonidas Koutsougeras Unit coordinator
Klaus Schenk-Hoppe Unit coordinator