92370 - LABORATORY OF MATHEMATICAL ECONOMICS

Conoscenze e abilità da conseguire

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.

Contenuti

1. 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. Lagrange multipliers and Kuhn-Tucker theory. Envelope theorem.

2. 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 products, norms, orthogonal subspaces.

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

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Students with good undergraduate background in maths should find some 75% of the topics familiar, though they will likely find the style and the perspective of the exposition new. This is the optimal configuration for benefiting from the course.

Students with less reliable undergraduate background in maths will find the course insufficient for filling the gaps in their knowledge. This is because the course is very dense and human brains are unable to efficiently interiorize a dense flow of abstract new knowledge within a period of time as short as two weeks. Such students are insistently encouraged to read in July and August chapters 6 to 18, 21, 23, 27, 29 and 30 of Simon and Blume (see the references below), such that during the two weeks of the course they can consolidate their knowledge.

The last lecture of the course has been moved to October 21st in order to maximize the number of attendees. It is dedicated to differential equations and most students with an undergraduate degree in economics will find the material new. Therefore, also students who are unable to attend the September classes should do their best to attend the last lecture.

Testi/Bibliografia

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.

Metodi didattici

Traditional lectures.

Modalità di verifica e valutazione dell'apprendimento

A final pass/fail test. A passing grade requires (1) a score of at least 66% at the test and (2) attendance of at least 75% of the classes.

Strumenti a supporto della didattica

The lectures will be recorded for the benefit of attending students but will not be streamed in real time.

A Virtuale page with selected course material will be made available.

Orario di ricevimento

Consulta il sito web di Iliyan Georgiev