This course aims to introduce students to optimization methods in a static context. The instruments, explained during the course, are crucial to describe the efficient behaviour of economic agents. Both unconstrained and constrained optimization methods will be presented during the course. At the end of the course students should be able to represent the behaviour of agents through the formalization of a constrained optimization problem and solve it using the mathematical results and the graphical approaches discussed during classes.
Expected learning outcomes
At the end of the course, the student will know the basic elements of the optimization theory in a static framework; will be able to formulate appropriate optimization problems; will possess an adequate mathematical terminology; will learn the main theoretical results and practical methods related to the optimization problems that can describe the behaviour of an economic agent.
1. Multivariate Calculus 1.a Gradients and Directional Derivateves 1.b Convex Sets 1.c Concave and Convex Functions 1.d Eigenvalues and Quadratic Forms 2. Static Optimization 2.a First and Second Order Conditions for Unconstrained Problems 2.b Constrained Optimization Problems: Equality Constraints First and Second Order Conditions 2.c Constrained Optimization Problems: Inequality Constraints First and Second Order Conditions 2.d Constrained Optimization Problems: Nonnegativity Constraints First and Second Order Conditions
Prerequisites for admission
Calculus I and Linear Algebra.
Lecture and tutorial
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3).
Assessment methods and Criteria
Written exam composed of practical exercises where the students have to choose the best method among those discussed in classes and apply them in a correct way.