### Course Syllabus

### Obiettivi formativi

Il Corso (42 ore di lezione frontale e 6 CFU) si propone di offrire conoscenze di base e specialistiche in materia di a) teoria e applicazioni della dualità nella sfera del consumo e della produzione; b) teoria delle scelte in condizioni di incertezza.

### Contenuti sintetici

Starting from the
assumption that students (are supposed to) have already acquired a sound
background in basic general microeconomics, the first part of this graduate
course intends to provide a comprehensive exposition of duality theory and its
applications in modern microeconomics. Consumer and producer optimization
(i.e. decision) problems will be analysed in both *R ^{2} *and

*R*dimensions in order to offer theoretical instruments useful for a better understanding of the methods and results of econometric models of consumer demand and production efficiency. The second part of the course will provide a graduate treatment of individual choice under uncertainty including measures of risk aversion, risk spreading and pooling.

^{N}Students should bear in mind that

a) Topics such as games and oligopoly form part of the program of
another microeconomic course (Advanced Microeconomics) delivered during the
second year. In order to avoid useless duplications they are not considered
here.

b) Topics such as moral hazard and adverse selection in the field of insurance will be covered in other courses (in particular Economics of Insurance/Economia delle Assicurazioni).

### Programma esteso

Contenuto dettagliato del corso

**Prima parte**

Individual consumer behaviour

· Hotelling-Wold identity

· Direct and indirect utility functions

· Roy’s identity

· Expenditure function and Slutsky decomposition

· Functional forms and estimations

· Distance function and its properties

· Relations between distance and direct utility functions

Producer behaviour

· Direct and indirect production functions

· The cost function and Slutsky decomposition

· Profit functions (unrestricted; restricted)

· Functional forms and estimations

· Input and output Distance function and their properties

· Measurement and estimation of production efficiency

**Seconda parte**

· Notion of uncertainty

· Choice under uncertainty and Axioms

· Properties of the utility function, risk premium and measures of risk aversion

· Measure of risk

· Comparative statics under uncertainty

· Production under uncertainty

· Price and technological uncertainty

### Prerequisiti

Calcolo intermedio (analisi I e algebra I) e microeconomia di base. Lo studente non basi la sua preparazione su testi di matematica per economisti.

Testo undergraduate di riferimento: H. Varian, *Intermediate Microeconomics*. *A modern approach*, Norton, ultima edizione

### Metodi didattici

Lezioni frontali. Esercizi individuli con correzione in aula.
Predisposizione del materiale didattico (testi e files di varia
tipologia) nella pagina e-learning del corso. Ricevimento con tutoraggio per piccoli gruppi (due ore settimanali).

All'inizio del corso verrà effettuato un test di ingresso.

### Modalità di verifica dell'apprendimento

Esame finale scritto (6 domande a punteggio differenziato, di cui 3 esercizi; ciascuna domanda è
suddivisa in più parti tra loro connesse). Non è prevista una prova intermedia. Non sono previste modalità particolari per studenti non frequentanti.

### Testi di riferimento

Bibliografia

**Per dualità**

R. Cornes, *Duality and modern economics*, Cambridge
University Press, 1992 (Chapters 2 – 8)

Or equivalent chapters in graduate textbooks

** Per incertezza**

H. Gravelle and R. Rees, *Microeconomics*, Prentice Hall, third edition,
2004 (Chapters 17 – 19). Or equivalent chapters
in graduate textbooks.

Basic online material with
exercises will be provided (please visit the E-Learning platform of the course). Language: Italian and English

### Periodo di erogazione dell’insegnamento

I semestre; II ciclo

### Lingua di insegnamento

Italiano

### Learning objectives

This (42h and 6 CFU) course intends to offer basic and specialized training in the following areas: a) duality in consumption and production: theory and applications; b) choices under uncertainty.

### Contents

Starting from the
assumption that students (are supposed to) have already acquired a sound
background in basic general microeconomics, the first part of this graduate
course intends to provide a comprehensive exposition of duality theory and its
applications in modern microeconomics. Consumer and producer optimization
(i.e. decision) problems will be analysed in both *R ^{2} *and

*R*dimensions in order to offer theoretical instruments useful for a better understanding of the methods and results of econometric models of consumer demand and production efficiency. The second part of the course will provide a graduate treatment of individual choice under uncertainty including measures of risk aversion, risk spreading and pooling.

^{N}Students should bear in mind that

a) Topics such as games and oligopoly form part of the program of
another microeconomic course (Advanced Microeconomics) delivered during the
second year. In order to avoid useless duplications they are not considered
here.

b) Topics such as moral hazard and adverse selection in the field of insurance will be covered in other courses (in particular Economics of Insurance/Economia delle Assicurazioni).

### Detailed program

**Detailed Content of the Course**

**First part**

Individual consumer behaviour

· Hotelling-Wold identity

· Direct and indirect Utility functions

· Roy’s identity

· Expenditure function and Slutsky decomposition

· Functional forms and estimations

· Distance function and its properties

· Relations between Distance and direct Utility functions

Producer behaviour

· Direct and indirect Production functions

· The Cost function and Slutsky decomposition

· Profit functions (unrestricted; restricted)

· Functional forms and estimations

· Input and output Distance function and their properties

· Measurement and estimation of production efficiency

** Second part**

· Notion of uncertainty

· Choice under uncertainty and Axioms

· Properties of the utility function, risk premium and measures of risk aversion

· Measure of risk

· Comparative statics under uncertainty

· Production under uncertainty

· Price and technological uncertainty

### Prerequisites

Intermediate mathematics including constrained optimization in R^{N }(Calculus I and basic matrix algebra) and basic microeconomics. Students are recommanded to avoid "maths for economists" textbooks.

Undergaduate referencee text: H. R. Varian, *Intermediate Microeconomics*. *A modern approach*, Norton, 8th (Eighth) edition.

### Teaching methods

Frontal class lectures. Individual execises with class solutions. Two hours of weekly small group tutorials will be organized.

On line material available (E-Learning course website).

At the beginning of the course an entry test paper will be organized.

### Assessment methods

Final written exam (6 questions with 3 exercises; each question includes subquestions). No differencs between attending and non-attending students. No mid-term exam. Due to the change of the lecturer, no past papers are available.

### Textbooks and Reading Materials

References

** For Duality**

R. Cornes, *Duality and modern economics*, Cambridge
University Press, 1992 (Chapters 2 – 8)

Or equivalent chapters in graduate textbooks

**For Uncertainty**

H. Gravelle and R. Rees, *Microeconomics*, Prentice Hall, third edition,
2004 (Chapters 17 – 19). Or equivalent chapters
in graduate textbooks.

Basic online material with
exercises will be provided (please visit the E-Learning platform of the course). Language Italian and English.

### Semester

I semester starting 10/12/2018.

### Teaching language

Italian

### Key information

- Field of research
- SECS-P/01
- CFU
- 6
- Term
- Primo Semestre
- Activity type
- Obbligatorio
- Course Length (Hours)
- 42
- Degree Course Type
- Corso di Laurea Magistrale