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

Linear spaces. Matrices, operations, rank and determinant. Inverse of a nonsingular square matrix. Linear systems, eigenvalues, eigenvectors, diagonalization theory.

Multivariate calculus. 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.

Time permitting: Differential equations. First order ordinary differential equations (separation of variables, linear equations). Difference equations

Testi/Bibliografia

Suggested references:

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

M. Osborne's tutorial "Mathematical methods for economic theory", available online: https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/toc

Metodi didattici

Lectures at the university premises

Modalità di verifica e valutazione dell'apprendimento

A final pass/fail test

Strumenti a supporto della didattica

Textbook, slides and exercises

Orario di ricevimento

Consulta il sito web di Annalisa Loviglio