**NEWS:**

PAOLO GHIRARDATO'S OFFICE HOURS: During the second semester, I am available to meet students (in room 5.22 of the School's building) on the following days:

- FRIDAYS, 11:30-13:00

I am also available by appointment. Send me an email by clicking here.

**SYLLABUS:** 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 economics; that is, some of the more fundamental results in the discipline of Economics.

The following is the planned syllabus for the course:

- 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]

**READINGS:**
The following are the suggested readings for the course (see the syllabus above for the specific chapters/sections used).

- 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University Press, Cambridge 1999 - Massimo Marinacci and Luigi Montrucchio, Notes on Calculus on Vector Spaces, unpublished manuscript

**EXERCISES:** The following exercises are **very important** as practice and verification of your understanding of the course material.

- Homework 1, with Solutions
- Homework 2, with Solutions
- Homework 3, with Solutions
- Homework 4, with Solutions
- Homework 5, with Solutions
- Homework 6, with Solutions
- Homework 7, with Solutions

**PAST EXAMS:** The following are some past exams for this course:

**CONTACTS**

paolo.ghirardato at unito.it

Created: 09/10/09. Last revised: 07/05/24