Mathematical Economics

Recommended Prerequisites

Undergrad Mathematics (Differential and Integral calculus) and Linear Algebra

Teaching Methods

Exposition of the theory, working examples and assignments. Timely provision of the slides of the lectures in electronic format.

Sets of exercises aimed at stimulating an active attitude by students in the different learning activities and contributing to their critical assessment, as well as the development of oral communication competences.

The continuous evaluation also includes several assignments and a final test covering the full program of the curricular unit.

Learning Outcomes

1. Calculate determinants, determine eigenvalues, evaluate the properties of matrices, interpret the meaning of the possible results.

2. Calculate limits and describe the properties of successions. Describe and evaluate the properties of sets. Apply differential calculus to the study of real functions. Demonstrate particularly important theorems.

3. Solve optimization problems. Discriminate and relate several optimizations methods. Integrate concepts of linear algebra in the resolution of optimization problems. Plan and justify the choice of optimization methods for the resolution of concrete problems.

4. Examine discrete and continuous dynamic systems, relating them with concepts of linear algebra and real calculus. Analyse the properties of systems selecting the adequate methods of analysis.

5. Describe and apply techniques of dynamic programming in the resolution of problems of dynamic optimization. Evaluate their use in the resolution of economic problems.

Work Placement(s)

No

Syllabus

1. Topics in Linear Algebra

2. The Rn Space and Multivariable Calculus:

a. Topology in Rn space

b. Multivariable Calculus

c. Static Optimization

d. Correspondences and Fixed Point Theorems

3. Differential and Difference Equations and Systems

4. Dynamic Optimization

a. Calculus of Variations

b. Control Theory

c. Dynamic Programming

Head Lecturer(s)

Pedro André Ribeiro Madeira Cerqueira

Assessment Methods

Assessment
The continuous evaluation also includes several assignments and a final test: 100.0%

Bibliography

Adda, J., and R. Cooper, 2003. Dynamic Economics. MIT Press.

Ljungqvist, L., and T. Sargent, 2004. Recursive Macroeconomic Theory. 2.ª ed., MIT Press.

Simon, C., and L. Blume, 1994. Mathematics for Economists. W. W. Norton.

Sydsaeter, K., Hammond, P., Seierstad, A., and A. Strom, 2005. Further Mathematics for Economic Analysis. Pearson Education.