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QUANTITATIVE METHODS FOR ECONOMICS - MOD. DYNAMIC OPTIMIZATION FOR ECONOMICS

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QUANTITATIVE METHODS FOR ECONOMICS - MOD. DYNAMIC OPTIMIZATION FOR ECONOMICS

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Academic year 2024/2025

Course ID
SEM0188B
Teacher
Paolo Ghirardato (Lecturer)
Year
1st year
Teaching period
Second semester
Type
Distinctive
Credits/Recognition
6
Course disciplinary sector (SSD)
SECS-S/06 - mathematical methods of economy, finance and actuarial sciences
Delivery
Formal authority
Language
English
Attendance
Optional
Type of examination
Written
Type of learning unit
modulo
Modular course
QUANTITATIVE METHODS FOR ECONOMICS - INTEGRATED COURSES (SEM0188)
Prerequisites
A good knowledge of basic calculus (at the level of Matematica I in the LT in Economia), linear algebra and of the basics of optimization (at the level of Matematica II in the LT in Economia).
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Sommario del corso

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Course objectives

This course  aims to develop the analytical tools which are fundamental for understanding Dynamic Programming and some important results in Mathematical Economics. 

Click on the link below (in the "Altre Informazioni") to be taken to this course's real web page (updated regularly).

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Results of learning outcomes

(stated by european descriptors with regard to this academic qualification (D.M. 16/03/2007, art. 3, comma 7) (Nota2) [Read at your own peril!]

-Knowledge and understanding. Expected outcomes: to learn to analytically and rigorously reflect on economic problems. Istruments: class-taught lessons and practice exercises presented by the lecturer. Examinations: practical and theoretical examinations in written form.
-Applying knowledge and understanding. Expected outcomes: With the immediate application of the mathematical tools provided by the course, the student will be able to face and solve a wide range of economic problems. Instruments: class-taught lessons and practice exercises presented by the lecturer. Examinations: practical and theoretical examinations in written form.
-Judgement autonomy. Expected outcomes: in the development of the analytics characterizing various models and through practice exercises the student gets familiarity, trust and thus judgement autonomy in the creation of models to analyse economic problems. Instruments: class-taught lessons and practice exercises presented by the lecturer. Examinations: practical and theoretical examinations in written form.
-Communicative skills. Expected outcomes: ability to communicate in written and oral form on the topics presented during the course. Instruments: class-taught lessons and practice exercises presented by the lecturer.
-Learning skills. Expected outcomes: ability to develop and apply new economic models. Instruments: class-taught lessons and practice exercises presented by the lecturer. Examinations: practical and theoretical examinations in written form.

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Program

This is a syllabus for the course (in [] the corresponding chapters of the suggested readings).

  • Preliminaries [Carothers, Chapter 1; Sundaram, Chapter 1 and Appendix B]
  • Basic notions of Topology in metric spaces [Sundaram, Chapter 1 and Appendix C; Carothers, Chapters 3-8]
  • The Weierstrass Theorem(s) [Sundaram, Chapter 3, Section 12.4; Marinacci-Montrucchio, Section 6.6]
  • Spaces of functions and the Contraction Mapping Theorem [Carothers, Chapters 10 and pagess 97-100; Sundaram, Section 12.4]
  • Convexity and separation [Sundaram, Chapters 1 and 7; Aliprantis-Border, Chapter 5]
  • The Maximum Theorem [Sundaram, Chapter 9]
  • Dynamic Programming I: Finite-horizon problems. The consumption-savings problem [Sundaram, Chapter 11]
  • Dynamic Programming II: The contraction mapping theorem, and infinite-horizon problems. The optimal growth model [Carothers, pp.97-99 for the Contr. Mapping Thm.; Sundaram, Chapter 12]

 

 

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Course delivery

The course-work is articulated in 48 hours of formal lecture time, and in at least as many hours of at-home work solving practical exercises.

 

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Learning assessment methods

Generalities:

The course grade is determined solely on the basis of written examinations.  The objective of the examination is to test the student's ability to do the following:

1) Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results 

2) Use effectively the concepts and the result to solve simple dynamic optimization problems in Economics.

 

Practicalities:

There are 5 possible exam sessions in each academic year. The first session takes place during the second semester (while the course is being taught), and it is articulated in a  midterm administered in early April and  and a final exam administered in mid-May. The remaining four sessions (from June until February) comprise a single comprehensive examination. The details for each type of examination are provided below.

Midterm+Final (April+May): Each of the two exams lasts 90 minutes, and it is articulated in 3 questions. Some of the questions have an essay part, and some of the questions also have a more practical ("exercise") part. Each question is scored 10 points, and the maximum score for the exam is typically 30. There is no minimum score in the midterm for admisssion to the final exam. Once both exams are graded, the final score in 60ths is computed, and it is transformed into 30ths, taking also into account the general class performance in the two exams (i.e, giving some weight to relative, as well as absolute performance) and normally counting a score over 50 as a perfect (i.e., 30/30) exam.

Comprehensive examinations (4 sessions between June and February): Each exam lasts 165 minutes, and it is typically articulated in 6 questions. Some of the questions have an essay part, and some of the questions also have a more practical ("exercise") part. Each question is scored 10 points, and the maximum score for the exam is 60. The final score in 60ths is computed, and it is transformed into 30ths, taking also into account the general class performance in the two exams (i.e, giving some weight to relative, as well as absolute performance) and normally counting a score over 50 as a perfect (i.e., 30/30) exam.

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Support activities

Weekly homework sets will be assigned (to be found on the course web page, see the URL in the "Note" below), and their solution will be posted and discussed in class.

Suggested readings and bibliography

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The following are the required textbooks for the Mathematics module:

  • R. Sundaram, A First Course on Optimization Theory, Cambridge University Press, Cambridge 1996
  • N.L. Carothers, Real Analysis, Cambridge University Press,Cambridge 1999
  • Massimo Marinacci and Luigi Montrucchio, Notes on Calculus on Vector Spaces, unpublished manuscript
  • C.D. Aliprantis and K.C. Border, Infinite-Dimensional Analysis, third edition, Springer-Verlag, 2007


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Notes

For further details, please consult the course's official web page:

http://sites.carloalberto.org/ghirardato/didattica/qme/qme.html

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