2016/2017

2018/2019

DM270

SECS-P/01 (POLITICAL ECONOMY)

DEPARTMENT OF ECONOMICS AND MANAGEMENT

ECONOMICS

PERCORSO COMUNE

3°

1st semester (24/09/2018 - 21/12/2018)

9

66 lesson hours

Italian

WRITTEN AND ORAL TEST

BERTOLETTI PAOLO (titolare) - 2 ECTS
GIORGI GIORGIO - 7 ECTS

The contents of the course Matematica Generale are considered as preliminary notions

The aim of the course is to provide the ability to use quantitative models in economics, with a special focus on the use of mathematical tools in economic analysis.

1) Linear algebra,
Vector space, bases, dimension. Linear functions and representation theorem.
Eigenvalues and eigenvectors: algebraic and geometric multiplicity. Necessary and sufficient conditions for linear independence of eigenvalues. Symmetric matrices. Diagonalization. Shur theorem Jordan canonic form. Cayley-Hamilton theorem.
Quadratic forms: classification and sign. Constrained quadtratic forms.
Spectral radius and power matrices series. Non-negative quadratic matrices and Perron-Frobenius theorem. Leontief and Sraffa models.
2) n-variable functions. Differential calculus for n-variable functions.
Partial derivatives and Jacobian matrix. Hessian matrix. Differentiable functions. Tangent hyperplane. Chain rule. Directional derivatives. Homogeneous functions and Eulero's theorem. Implicit functions' theorem. Taylor's formula.
3) Optimization. Unconstrained and constrained problems. Weierstrass Theorem.
uncostrained problems: Fermat theorem. Second order sufficient conditions.
(Strictly)convex and concave functions. their caracterization.
Application to uncostrained optimization. Quasiconvex and pseudoconvex functions. and their caracterization. Optimality under equality constrain. lagrange multipliers method: necessary and sufficient optimality conditions. economical interpretation of multipliers. Non-linear programming. Gordabn's theorem. Abadie and Fritz-John necessary optimality conditions. Constrains' qualification conditions. Kuhn-Tucker's necessary conditions. convex programming a lagrangian's saddle points. Linear programmin. Dual problem. Weak and strong duality results.
4) Dynamical systems Continuous and discrete dynamical systems
differential equations. Systems of first order differential equations. theorem of existence and uniqueness of solution for the Cauchy problem. Linear equations. Systems of linear equations with constant coefficients. equilibrium solutions and their stability.

Lessons

G. Giorgi, Matematica per l'Analisi Economica e Finanziaria, Giappichelli, Tiorino, 2017.
De Giuli, M.E., Giorgi G, Maggi A. M., Magnani U., Matematica per l'Economia e la Finanza, Zanichelli, Bologna, 2008.

Written exam (2 hours), short statement on topics developed during classes and oral exam