MATHEMATICAL MODELS FOR BUSINESS
Italian and, if requested, English
The aim of the course is to provide a base of knowledge of some mathematical tools for economics and management science for gainful employment in economic growth and optimal planning. In particular, some instruments for solving unconstraint and constraints optimization problems will be treated. The course also aims at achieving the educational objectives to enable students in entering the labor market with skills for using mathematical results/instruments as a valid support in taking business decisions in the different functional areas.
Expected learning outcomes
Knowledge and understanding:
The student should demonstrate to know the principal concepts and instruments for modelling some economic problems.
Applying Knowledge and understanding:
The student should demonstrate to know how to handle the main mathematical results/instruments for solving unconstraint and constraint optimization problems.
The student should have the maturity and the ability to choose autonomously the more suitable mathematical result/instrument to solve a specific problem.
The student should be able to communicate clearly and with an adequate technical language the contents of the course.
Lifelong learning skills:
The student should be able to show a good learning ability and autonomy in investigating in-depth the matters of the course using the references provided by the teacher.
Functions of several real variables
Basic definitions - Continuous functions - Differentiability - Taylor’s formula.
Concavity and Convexity
Convex, concave sets - Convex, concave functions- First order conditions- Second order conditions - Some economic applications.
Definitions- First order conditions- Second order conditions. Some economic applications.
Equality constrains - Lagrange’s Theorem, geometric interpretation- Lagrangian multipliers, geometric and economic interpretation- Some economic applications.
Functions of several real variables, differentiability, concavity and convexity. Some economic applications (20 hours).
Unconstrained Optimization (8 hours).
Constrained Optimization. Some economic applications (12 hours). Exercises (8hours).
Traditional lectures, analysis of case studies, and exercises. Business and economic topics as well as the mathematical tools and instruments will be discussed during the lessons. The discussion of study-cases and exercises enable the students to select and apply the more suitable mathematical instruments to explore business and economic dynamics in a quantitative viewpoint.
Simon Blume, Matematica 2 per l’economia e le scienze sociali, Università Bocconi Editore.
Guerraggio-Salsa, Metodi matematici per l'economia e le scienze sociali, Giappichelli
The degree of learning is constantly assessed during the course submitting to the students exercises and case studies related to business context and economic dynamics. Final written and oral assessments about all the topics covered in the program. Beyond exercises that are contextualised in real problems, the written assessment also includes open-ended questions. Moreover, the written assessment is integrated with the oral assessment by a discussion of the test and/or an in-depth assessment on all the topics of the program.