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

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

Readings/Bibliography

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

 

Teaching methods

Lectures at the university premises

Assessment methods

A final pass/fail test

Teaching tools

Textbook, slides and exercises

Office hours

See the website of Annalisa Loviglio