LEARNING OUTCOMES

The course aims to provide students with a basic knowledge about the main quantitative methods to support  decision-making processes in  economics, both in certain and uncertain environments. The course also aims to let the students be able to use the reference software environments for solving the different problems faced. From a methodological point of view will be introduced single decision maker optmization problems, in particular using convex programming models to optimize different objective functions (such as profit and utility maximization and cost minimization), decision models under uncertainty and risk and game theory decision methods to deal with situations of strategic interaction. 

AIMS AND LEARNING OUTCOMES

The course aims to present the subject in its theoretical, methodological and applicative features in order to provide students with knowledge of the applicable models and methodologies. The practical laboratories aim to provide the student with the knowledge and skills to use specific software in order to solve the practical problems faced.

At the end of the course the students should have acquired skills that allow them to understand, describe and solve different types of real problems, developing models and solution methods and using, with a certain mastery, the reference software environments.
In particular, students at the end of the course will:

• Know and understand the main tools and methods of decision analysis that allow them to formalize individual decisions in the economic and social application field.
• Know the main elements of a problem of choice in terms of decision makers involved, type of data available, variables, constraints and objectives.
• Apply the acquired knowledge to describe, formalize and solve the problems and the related single-decider optimization models as well as those with social and economic interaction components in situations of applicative interest.
• Use both the conceptual and the operational level of the knowledge acquired with independent evaluation and critical reasoning skills, developing original models applicable in different application contexts.
• Have acquired a correct terminology and technical language to clearly communicate the main elements of the decision problem under consideration.
• Have acquired useful skills in the field of applied mathematics to access the most quantitative master's degree classes in the economic and quantitative area.
• Have developed learning skills that will allow them to deepen and apply independently the main topics of the discipline in the working contexts in which they will operate.

PREREQUISITES

Suggested: Mathematics and Statistics

TEACHING METHODS

Lectures, analysis of case studies, computer lab exercises and lessons using ad hoc software tools.

In the case of health emergency situation, the updated distance and blended teaching methods will be communicated on the Aulaweb page of the course (registration is required and recommended).

SYLLABUS/CONTENT

For each part of the course, the theoretical discussion intended to provide basic theory content, will be complemented by the practical/laboratory part in the computer lab using specific software tools (Excel solver and optimization software).

Part I:

• Introduction to decision-making and problem solving: from real problems to mathematical models.
• Decision models classification.
• Introduction to non-linear, convex, linear and integer mathematical programming.
• Resource allocation problems arising in the production of goods and services
• Supply and demand matching problems
• Linear programming, duality, economic interpretation and sensitivity
• Introducing non-linear hypotheses on prices and costs

Part II:

• Study of functions in several variables: unconstrained maxima and minima.
• Constrained optimization, Lagrangian functions and economic interpretation of Lagrange multipliers.
• Consumer choice models and utility maximization.
• Company choice models: cost minimization and profit maximization.
• Models for selecting investments in risky conditions.

Part III: 

• Decision trees and decision theory in conditions of uncertainty and risk.
• Optimization of the expected economic value of decisions.
• Utility Theory.
• Introduction to Game Theory.
• Study and modeling situations of strategic interactions (Pure and mixed strategies). Game theory and optimization.

RECOMMENDED READING/BIBLIOGRAPHY

The text books and other additional handouts for foreign students will be communicated at the beginning of the course and published on the course Aulaweb page