92370 - Laboratory Of Mathematical Economics

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

Functions of one real variable, domains, limits, derivatives, definite and indefinite integrals and related solution methods.

First order differential equations solved through separation of variables, variation of constants and changes of variables. Some notions on higher order differential equations, difference equations and dynamical systems.

Functions of 2 or several real variables, partial derivatives, tangent hyperplane, Hessian matrix and stationary points. Surfaces in a 3-dimensional space.  Constrained and unconstrained optimization. Methods of Lagrange's multipliers and Kuhn-Tucker Theory. Utility functions and applications to Economics.

Linear Algebra: matrices, vectors, vector spaces and subspaces, 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, properties of matrices.

Readings/Bibliography

Fundamental Methods of Mathematical Economics, Alpha C. Chiang, Kevin Wainwright, McGraw-Hill, 2004.

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

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

A First Course in Optimization Theory, Rangarajan K. Sundaram, Cambridge University Press, 1996.

Teaching methods

Traditional lessons in the classroom.

Assessment methods

Non-mandatory final test including exercises to solve.

Teaching tools

No particular tool.

Office hours

See the website of Arsen Palestini