# ECONOMICAL MODELLING AND ENVIRONMENTAL POLICIES

## Learning outcomes of the course unit

The new and reinforced sensibilities for the environmental issues at global level need deeper economic and quantitative skills capable to evaluate the effects of environmental policies on environmental resource availability. The aim of this course is to provide a set of theoretical and operational skills to face, develop and solve decision problems into the environmental policy framework, throughout models based on economics theory and mathematical programming tools. By the way of the course, the student can acquire knowledge about methods and operational tools for evaluating the economic relationships between economic activities and environmental resources. In particular, the study of mathematical optimization techniques will provide to the student a support for facing the problem linked to environmental policy evaluation with respect to the economic agent behaviour.

## Course contents summary

The course aims to provide a series of theoretical and practical knowledge on mathematical programming models for the efficient management of environmental resources. The course is divided into 3 parts. The first part presents the technique of mathematical programming in the economic theory framework. Some microeconomics reminds will help the interpretation of the economic problems by mathematical programming. The second part of the course provides the techniques for the construction of mathematical programming models. The Tableau technique and the duality will be the guides for the analytical model development. The third part of the course focuses on the tools to solve the problems of mathematical programming. In particular, the simplex algorithm will be applied through the use of spreadsheets and GAMS (General Algebraic Modeling System). All applications and exercises will be undertaken in relation to the management of environmental resources and the implementation of environmental policies.

## Course contents

1. The Linear Programming (LP)

1.1 Economic principles of linear programming

1.2 LP problem formulation

1.3 The duality

1.4 The information organization using the TABLEAU

1.5 LP problem solving: the simplex algorithm

1.6 LP and Langrange function

2. Quantitative tools for developing LP models

2.1 The GAMS (General Algebraic Modeling System) language for mathematical programming model formulation

2.2 Exercises on pc

3. The analysis of environmental issues using mathematical programming

3.1 The environmental performance analysis throughout models for technical and economic efficiency evaluation.

3.2 The economic agent behaviour facing environmental policy: the study of a positive mathematical programming approach

3.3 Exercises on pc.

## Recommended readings

Recommended readings

- Quirino Paris, An economic interpretation of linear programming, Iowa State Press, Ames, 1991;

- Richard Rosenthal, GAMS: a user’s guide, Gams Development Corporation, Washington, 2008;

- Documents distributed by the lecturer.

## Teaching methods

Acquisition of knowledge: lectures, seminars and optimization package teaching

Acquisition of the ability to apply knowledge: exercises with PC

Acquisition of judgment: During the course students will be encouraged to develop a capacity for critical analysis and evaluation methods.

Acquisition of learning skills: Along the learning process, the student will deal with the application of the knowledge acquired through exercises planned.

Acquisition of technical language: students will learn the meaning of the terms commonly used in the context of the operational research applied to environmental resources.

## Assessment methods and criteria

The exam is in written form and divided into two parts. The first part (2 hours) consists of two open questions, including one designed to test the knowledge acquired on the theory of mathematical programming, and the second concerning the application of mathematical programming models in the context of environmental issues . The open form of the two questions used to assess the ability of the student to trace the links between economic theory and analytical techniques of optimization behavior. The answers to the two questions are valued in thirty. The second part of the exam (3 hours) is an exercise of mathematical programming to set up and solve with the techniques learned during the course and with the support of specific software for mathematical programming. The aim of the second part is to evaluate the ability to apply the constrained optimization techniques for the efficient allocation of scarce environmental resources. The maximum score assigned to the exercise is 30 points. The final assessment of the exam is calculated as the average of the two final scores.