## Further Mathematical Methods for Economics

Module code: ECN212 and ECN307

This module introduces students to further topics in mathematics beyond the level reached in ECN118 and ECN119. The material to be covered will include topics from matrix algebra, constrained optimisation and inequality constrained optimisation.

These techniques will be applied to a range of problems in economics such as elasticity of substitution, oligopoly modelling and duality.

### Aims of the module

The aims of the module are:

• to build upon a basic knowledge of mathematical economics, introducing and explaining some of the more advanced mathematical techniques that are prevalent in modern economics
• to show how these mathematical techniques can be applied to intermediate economic analysis and discussions

### Learning objectives

(provisional)

By the end of the module you should demonstrate an understanding of, and be able to apply in a variety of economic situations, the principles of:

• univariate and multivariate calculus
• integration and differential equations
• linear algebra
• constrained and unconstrained optimisation and comparative static analysis (with and without the use of linear algebra)
• basic inequality constrained optimisation
• maximum value functions and the envelope theorem

### Syllabus

(provisional)

Calculus: partial and total derivatives, differentials, implicit functions, concavity and convexity, integration and differential equations

Optimisation: single variable and multivariate, unconstrained, equality and inequality constrained, multiple constraints, value functions, envelope theorem

Linear algebra: eigenvalues and eigenvectors, quasiconcavity. Hessians and bordered Hessians, quadratic forms, comparative statistics

Economic examples: elasticity of substitution, generalised oligopoly models, duality in consumer theory

### Teaching methods

Lectures and Workshops

### Assessment

Unseen three-hour examination worth 100% of the total mark which takes place at the end of semester two.

We advise you not to buy books before the module begins, as the reading list may change. If you wish to read in advance, look for these texts in the University library

Chiang, AC; Wainwright, K (2005) Fundamental Methods of Mathematical Economics, 4th edition, McGraw-Hill

Further information will be given during the course

Prerequisites Restricted to students for whom it is core or approved. As an option a mark of 60 or above in ECN118 or ECN119 is required, or equivalent qualifications