Two - Year Master Degree in Economics

QUANTITATIVE METHODS FOR ECONOMICS - MODULO DI MATHEMATICAL ECONOMICS

Quantitative Methods for Economics - Mathematical Economics

Academic year 2020/2021

• QUANTITATIVE METHODS FOR ECONOMICS CORSO INTEGRATO (SEM0058)

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Support activities
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

This course is a 6-credit module of a 2-module (12 credit) course aimed at introducing and developing many of the analytical tools which are used throughout theoretical and applied Economics. In this module, particular stress will be posed on the development of the analytical tools necessary for understanding and proving some of the basic results in general equilibrium theory and in dynamic macroeconomics, that is, some of the more fundamental results in the discipline of Economics.

Results of learning outcomes

At the end of the course, the student is expected to be capable of:

-using the basic tools and results to pose, formalize and solve an economic model

-knowing the extent to which the results obtained in the previous step are dependent on the assumption that s/he has made about the behavior of the economic agents

-knowing therefore the extent to which the results are suggestive of real-world economic phenomena

-being able to think about possible and useful generalizations of the posited model

-being able to communicate such findings using appropriate and clear mathematical notation and language

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. 

For the duration of the Covid-19 emergency, the lectures are held online according to the official course schedule: Thursdays 11:15-13:15, Fridays 14-17. Please contact me via email to be sent an invitation for the online lectures.

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 answer questions in basic general equilibrium analysis --e.g., proving the existence and structure of an equilbrium of an economy-- or similar issues --e.g., solving a simple dynamic consumption-saving problem

Practicalities:

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

Midterm+Final (May+June/July): Each of the two exams lasts 90 minutes, and it is articulated in 3 questions. Each question has an essay part, and some of the questions also have a more practical ("exercise") part. Each question is scored 0-10, so that the maximum score for each exam is 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).

Comprehensive examinations (4 sessions between July and February): Each exam lasts 165 minutes, and it is articulated in 6 questions. Each question has an essay part, and some of the questions also have a more practical ("exercise") part. Each question is scored 0-10, so that 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).

Covid-19 Adjustments: For the duration of University lockdown due to the Covid-19 health emergency, the exam sessions will be held via video-conferencing (using the Webex technology) rather than in-person. The exam format will be the same as described above, but students will be asked to write the exam(s) in the course of a Webex conference with their video-camera on for the whole duration of the exam, and they will be expected to be able to transmit a scan or photo of their exam by the end of the exam. In the event of significant interruption of the video-feed (on the side of the student) the written exam will be annulled and substituted by an oral interview. Students who foresee problems with the video-confering setup should get in touch with the instructor as soon as possible to discuss alternative arrangements. Students should also take the time to read the reminder [in Italian] on UniTo's ethical code included in the Notes section below.

Support activities

Weekly homework sets will be assigned, and their solution will be posted and (if time allows) discussed in class.

Program

[Please refer to the course's web page, indicated in the "Notes" below for a more up-to-date syllabus and reference list]

Part I: Topology in Metric Spaces

-Metrics and norms, metric spaces and normed spaces

-Topological notions in metric spaces, open and closed sets, sequences and convergence

-Continuity and its characterization

-Connectedness, completeness and compactness, and their consequences for continuous functions

Part II: Some Mathematics for Economics

-A brief look at constrained optimization, with equality and inequaliy constraints

-Convexity of sets and functions, and the separating hyperplane theorems

-Fixed point theorems and the contraction mapping theorem

Part III: Applications

-Basic results on General Equilibrium analysis

-A dynamic choice problem

[Please refer to the course's web page, indicated in the "Notes" below for a more up-to-date syllabus and reference list]

The following are the required readings for the course:

-N.L. Carothers, Real Analysis, Cambridge University Press,Cambridge 1999, Chapters 1-8 and 10
-Massimo Marinacci and Luigi Montrucchio, Notes on Calculus on Vector Spaces, unpublished manuscript, chapters 9 and 10 and section 6.6
-C.D. Aliprantis and K.C. Border, Infinite-Dimensional Analysis, third edition, Springer-Verlag, 2007, part of Chapter 5

Class schedule

Note

Official course web page

Online exams and the University's ethical code: If you understand Italian, please read the following reminder (if you don't: it basically says that cheating in exams is a serious crimimal offense, and that we will pursue it with the same attention as always):

Ogni studente/essa è invitato/a a leggere con attenzione il Codice etico di Ateneo (disponibile al link: https://www.unito.it/sites/default/files/allegati/01-08-2014/cod_etico_comunita_universitaria.pdf) nei cui principi morali – a maggior ragione in questa situazione, nella quale le modalità di esame che dovremo adottare vi responsabilizzano di più – siamo tutti sicuri che vi riconoscete. Siete uomini e donne che presto troveranno collocazione nel mondo del lavoro: noi docenti abbiamo cieca fiducia nelle vostre qualità umane e a quelle ci appelliamo.

Tuttavia il rischio che i principi meritocratici vengano inquinati da condotte non consone è immanente ed è per tale ragione che ciascun docente continuerà, con ancora maggiore rigore, a sorvegliare lo svolgimento delle prove di esame, orali e scritte, agevolato dagli strumenti di analisi inferenziale dei numerosi dati a nostra disposizione e dei software anti-plagio e anti-copiatura (per es. TURNITIN https://www.unito.it/node/4686), per evitare che il rispetto del merito sia appannaggio solo di alcuni.

Oltre che moralmente riprovevoli, sono comportamenti anche illeciti che saranno puniti nei modi e con le sanzioni amministrative che il regolamento su Procedimento e sanzioni disciplinari nei confronti degli studenti prevede (https://www.sme.unito.it/sites/u005/files/allegatiparagrafo/20-07-2016/regolamento_sanzioni_disciplinari_scuola_di_management_ed_economia_0.pdf)

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