# 92370 - Laboratory Of Mathematical Economics

### Course Unit Page

• Teacher Iliyan Georgiev

• Learning modules Iliyan Georgiev (Modulo 1)
Iliyan Georgiev (Modulo 2)

• Credits 3

• SSD SECS-S/06

• Teaching Mode Traditional lectures (Modulo 1)

• Language English

• Campus of Bologna

• Degree Programme Second cycle degree programme (LM) in Economics (cod. 8408)

• Course Timetable from Sep 06, 2021 to Sep 17, 2021

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda. ## Learning outcomes

At the end of the course the student has reinforced the mathematical reasoning and acquired the necessary skills and ability to work on the mathematical structures of a wide range of economic models. In particular, he/she is able to experience the deep knowledge of a mathematical problem and to comprehend the rigorous logic on which it is based. Furthermore, he/she is able to: - determine and discuss the nature of stationary points of several variables functions, recurrence relations and differential equations, thereby deducing properties of models' steady states; - identify and interpret different kinds of economic dynamics and investigate the related models; - work with Linear Algebra basic tools to construct and solve problems involving eigenvalues and eigenvectors; - formulate Definitions of necessary tools such as equilibrium concepts to be applied in many economic frameworks such as Industrial Organization, Contract Theory, Voting Systems, Game Theory, Macroeconomic Theory; - write correct proofs of Propositions and Theorems.

## Course contents

Linear spaces. Matrices, operations, rank and determinant. Inverse of a nonsingular square matrix. Linear systems, kernel of a matrix, linear maps, eigenvalues, eigenvectors, diagonalization theory. Scalar product, norm, orthogonal subspaces.

Functions of one and several real variables: continuity, convexity, quasi-convexity, (partial) derivatives, differentiability, tangent line/hyperplane, stationary points, Hessian matrix. Constrained and unconstrained optimization. Methods of Lagrange's multipliers and Kuhn-Tucker Theory.

Indefinite and Riemann integrals in one variable. First order ordinary differential equations (separation of variables, linear equations). Some notions of difference equations and dynamical systems.

Mathematics for Economists, Carl P. Simon, Lawrence Blume, Norton & Company, New York, London, 1994.

Essential Mathematics for Economic Analysis, Peter Hammond, Knut Sydsaeter, Prentice-Hall, Harlow, 2008.

Further Mathematics for Economic Analysis, Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Prentice-Hall, Harlow, 2008.

## Assessment methods

A pass/fail final test

## Teaching tools

A dedicated page on Virtuale

https://virtuale.unibo.it/course/view.php?id=31810