## Trinity College Dublin, The University of Dublin

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# Mathematical Economics

## Module Code: EC3080

### Module Title: Mathematical Economics

• ECTS Weighting: 10
• Semester/Term Taught: Michaelmas + Hilary Term
• Contact Hours: 44 hours of lectures and 10 hours of tutorials
• Module Personnel: Lecturers: Professor Paul Scanlon (MT) / Lecturer - Professor Alejandra Ramos (HT)

### Module Learning Aims

The first half of the module covers topics in optimization in both dynamic and static settings. In particular, one goal of this half of the module is to show how mathematical techniques may be applied to economic modelling. Particular emphasis is placed on the application of advanced mathematical methods to standard neoclassical production and consumption theory.

The second half of the module covers topics in linear algebra. The purpose of this module is to extend the treatment of linear algebra given in the Senior Freshman Mathematical and Statistical Methods module, and to study some of the applications of linear algebra and vector calculus in economics. The extensions are concerned with more rigorous exposition of a range of results in matrix algebra and vector space theory.

### Module Content

Topics discussed during Michaelmas Term:

• Kuhn-Tucker Optimization in Static and Dynamic Settings
• Differential Equations
• Difference Equations
• Applications of Integration
• Approximation Theory

Topics discussed during Hilary term:

• Systems of Linear Equations and Matrices
• Determinants
• Eigenvalues and Eigenvectors
• Quadratic Forms and Definite Matrices
• Vectors and Vector Spaces
• Algebra and Geometry of Ordinary Least Squares
• Applications

### Learning Outcomes

On successful completion of this module, you will be able to:

• Formulate economic problems mathematically;
• Apply mathematical techniques to economic problems in both dynamic and static settings;
• Interpret mathematical formulations of economic problems;
• Derive and draw economic insights from solutions to mathematically formulated economic models;
• Program MATLAB code to represent and solve some mathematically formulated economic problems.

Satisfactory completion of this module will contribute to the development of the following key skills:

• Ability to understand mathematical representations of economic models;
• Ability to represent economic dynamics in mathematical form;
• Ability to quantify insights from economic models;
• Ability to synthesize different mathematical techniques when solving economic problems.

Michaelmas Term:

• Chiang, A.C. and Wainwright, K., Fundamentals of Mathematical Economics (4 th edn.), McGraw-Hill, 2005.
• Hoy, Michael et al., Mathematics for Economics, 3rd ed., MIT Press.

Hilary Term:

• Anton, H. and Rorres, C., Elementary Linear Algebra: Applications Version, (10th/11th edn.), Wiley, 2010/2014.

EC2040

### Assessment Details

There will be a term test in Michaelmas Term and Hilary Term each accounting for 10% of the overall grade. The annual exam is worth 80% of the overall grade.

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