GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
First Part: BUSINESS ADMINISTRATION
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identities. Types of firms.
2) The firm in its economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and profitability. Information Systems Governance and Internal controls (overview). Planning in business (overview).
Second Parte: ACCRUAL ACCOUNTING
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

First Part: Business Administration
Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2° edizione, 2021
Onida, P., Economia d'azienda, Utet, Torino, 1970
Zanda, G., Lineamenti di Economia Aziendale, Edizioni Kappa, Roma, 2006

Second Part: Accrual Accounting
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2° edizione, 2020
For business administration and accounting exercises:
Paoloni M. (a cura di), Mattei G., Paoloni, N., Eserciziario di economia aziendale e contabilità, CEDAM, 2018

Syllabus
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Robert N. Anthony – Leslie K. Breitner, Essentials of Accounting, Prentice Hall, 2007
Slides/teaching notes will be available on the website

1. National accounting system: basic defintions and identities. Main macroeconomic indicators
2. Keynes’s theory: aggregate demand and equilibrium output
3. Keynes’s theory: money and interest
4. The IS-LM model
5. The AS-AD model
6. Inflation and unemployment
7. Macroeconomics of the European Union
8. Money: creation and control

Compulsory material:
1) Textbook: Antonella Stirati, Fondamenti di macroeconomia, Giappichelli, ISBN 9791221108514 (forthcoming in September 2024. Check the detailed programme for precise indications on the parts of the textbook to be studied). Students may ask for alternative material in English. Please contact prof Palumbo
2) Additional teaching material (lecture notes, slides, etc, made available on the moodle website)

The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

Fondamenti di Macroeconomia, elementi di base, di Antonella Stirati; Giappichelli 2024

Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.
Limits:
Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Integral calculus:
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

Suggested materials:
- Notes can be downloaded online from the course Matematica Generale on Moodle at the website: https://economia.el.uniroma3.it/
Optional materials:
- Loretta Mastroeni, Alessandro Mazzoccoli, Pierluigi Vellucci. Esercizi di matematica generale. Esculapio, 2023

Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.

Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.

Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.

Real functions of a real variable:

Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.

Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.

Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).

Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).

Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.

Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.

Linear algebra:

Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.

Integral calculus:

Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(w.p.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.

(w.p.) = “with proof”

Suggested materials:

- Mastroeni, Mazzoccoli, Vellucci: "Esercizi di matematica generale". Società editrice Esculapio. ISBN 9788893853910

Optional materials:

-Peccati, Salsa, Squellati. "Matematica per l'economia e l'azienda". Egea.

-Bramanti, Pagani, Salsa. Calcolo infinitesimale e algebra lineare Seconda edizione

- Alberto Bersani, Francesco Manzini, Loretta Mastroeni. Esercizi di Matematica Generale: Per i corsi del nuovo ordinamento delle Facoltà di Economia. Società Editrice Esculapio, 2009.

Introduction to computer science
Computer architecture
CPU, main memory, secondary memory, input/output peripherals
The operating system and application software
Overview of text document editors
Creating and managing text documents
Tools for formatting text, images, tables, and styles in text documents
Review capabilities of a text document
Advanced features for text documents
Spreadsheet overview
Cells, formulas and major spreadsheet features
Using functions and constructing charts in spreadsheets
Advanced features for spreadsheets

Materials provided by the lecturer

The program includes:
Introduction to law
Forms of State and forms of Government
Beyond the State: the EU
The sources of law
Parliament and its functions
Institutes of direct democracy
The abrogative referendum.
The Government and its functions
The President of the Republic and his attributions
Principles on the subject of Administration
The other organs
Local ordering
Rights and freedom
The economic Constitution
Judicial power
Constitutional Justice

It is recommended the study of one of the following books:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, latest edition
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, latest edition
F. Modugno (a cura di), Diritto Pubblico, Torino, Giappichelli, latest edition
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, latest edition

The Public Law course is divided into two modules.
Module I covers the following topics: theory of social groups; the normative social groups; the structure of the legal system; power and its species; power-sharing techniques; the forms of exercise of power: the legal norm and the provision; subjects; interests; the goods; subjective legal situations; the legal facts; human behaviors; the legal effects; the responsability; the regulatory levels of government (international, European Community, state, local); the organization of public authorities; public functions (political direction, regulation, administration, jurisdiction).
The II Module deals with the Italian legal system and the regulatory principles of its political, legislative, administrative and jurisdictional activity.

For preparation for Modules I and II we recommend studying a manual chosen from the following:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, ult. ed.
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, ult. ed.
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, ult. ed.

Detailed program by chapters.
Part 1. Introduction
Chapter 1. Thinking as an economist (all)
Chapter 2. Supply and Demand (All)
Part 2. Consumer theory.
Chapter 3. Rational consumer choice (all but par. 3.5)
Chapter 4. The utility function (all except par. 4.6.4)
Chapter 5. The applications of rational choice and demand: paragraphs 5.4 and 5.4.1 only.
Part 3. Business theory and market structure.
Chapter 9. Production (all). Appendix to Chapter 9: A.9.1, A.9.2, A.9.2 only
Chapter 10. Costs (all except Section 10.7)
Chapter 11. Perfect competition (all except 11.11.1, 11.12.1, 11.12.2, 11.12.3, 11.14)
Chapter 12. Monopoly (all but paragraph 12.9)

R.H. Frank e E. Cartwright (2021) Microeconomia, VIII edizione. Milano: McGraw-Hill

Elements of the theory of production
- inputs, outputs and production methods
- the subsistence economy
- the economy with a surplus
The surplus approach to commodity value and income distribution
- the relevance of social and institutional elements to income distribution
- the explanation of the real wage rate
- the "core" of the classical approach
- the link between profit rate and relative prices
- the price equations
- the classical theory of rent
The theory of consumer choice
- budget set and budget constraint
- preferences
- consumer choice
- consumer-good demand curves
The theory of firm choice
- the function of production
- profit maximisation
- isoquants and isocosts
- the output expansion path and long-term cost curves
Production factors and the marginalist explanation of income distribution
- marginal and average productivity of factors
- the demand curves of factors of production
- equilibrium between supply and demand for factors of production
Market forms
- perfect competition
- monopoly
- Cournot oligopoly
- Stackelberg oligopoly
Introduction to the welfare economics
- allocations and Edgeworth box
- Pareto improvements and Pareto optima
- first theorem of welfare economics

i) “Elementi di teoria della produzione”, Dispensa n. 1 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
ii) “La teoria classica della distribuzione e dei prezzi relativi”, Dispensa n. 2 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
iii) “Teoria marginalista della distribuzione”, Dispensa n. 3 (materiale didattico redatto da S.M. Fratini).
iv) Frank Robert H.; Cartwright Edward; Piras R. Microeconomia. McGraw-Hill Libri Italia, Milano. 2021.
v) “Glossario ed Esercizi Svolti di Microeconomia” (materiale didattico redatto da S.M. Fratini e D. Pignalosa).

An introduction to the fundamental ideas of statistics. Topics include:

Descriptive statistics: graphical summaries of data, measuring the center of quantitative data (mode, median, mean), measuring the variability of quantitative data (standard deviation, variance), simmetry of a distribution (Fisher coefficient), the association between two variables (chi-square), the association between two quantitative variables (covariance, correlation coefficient).

Probability: probability of events (probability of the complement of an event, of the union and intersection of two events, conditional probability, independent events, Bayes theorem), discrete and continuous random variables (the Bernoully r.v., the Binomial r.v., the Poisson r.v., the Normal r.v., the Student t r.v., che Chi-square r.v.).

Inferential statistics: sample versus population, sampling distributions, point and interval estimates of population parameters, confidence intervals for a population mean and a proportion, significance tests about hypotheses on a population mean and a proportion, p-values.

Regression analysis: the regression line, ordinary least squares, describing the strength of the association, nonlinear regression models, confidence intervals and tests on the parameters of the regression line, prediction.

G.Cicchitelli, P.D'Urso, M.Minozzo. Statistica: principi e metodi. Pearson, fourth edition:
Chap. 1 (excluding 1.11), Chap. 2 (excluding 2.4, 2.5), Chap. 3 (excluding 3.4, 3.5, 3.6), Chap. 4 (excluding 4.3, 4.4, 4.5, 4.6, 4.15), Chap. 5 (excluding 5.3, 5.6, 5.7, 5.8), Chap. 6 (excluding 6.3), Chap. 9 (excluding 9.3), Chap. 10, Chap. 11 (excluding 11.2.1), Chap. 12, Chap. 13, Chap. 14 (excluding 14.2, 14.6, 14.7),Chap. 17 (excluding 17.6), Chap.18 (excluding 18.3, 18.4), Chap. 19 (excluding 19.5), Chap. 20 (excluding 20.6, 20.7), Chap. 22 (excluding 22.2.2), Chap. 23.

A collection of exercises by the teacher is available to students on Moodle.

Descriptive statistics:
variables and their measurement, univariate distributions, describing data with tables and graphs, measures of position, variability.
Bivariate descriptive statistics: independence, association, correlation, probability distributions for discrete and continuous variables, sampling distributions
Inference: estimation, hypothesis test, regression

A. Agresti, B. Finlay. Statistical methods for the social sciences. Pearson International Edition-4th edition (2009)

Part 1 - The theory of Financial Statements
-Introduction to the study of the Financial Statements
- The basic functions of the Financial Statements
- The nature of income and capital
- The purposes of the Financial Statements
- The relationship between income, evaluation criteria and purposes of the Financial Statements
- The goals of the Financial Statements in corporate doctrine: the "alpha" goal and the "beta" goal

Part 2 - The Financial Statements according to the Civil Code
- The Financial Statement documents - Structure and content (Articles 2423-ter - 2425 of the Italian Civil Code)
- The general clause and the principles for preparing the Financial Statements (articles 2423 - 2423-bis of the Italian Civil Code)
- The specific evaluation criteria (art. 2426 of the civil code)
- Fixed assets
- Receivables
- Inventories (Lifo, Fifo, Cmp)
- Work in progress assets
- The content of the Notes and the Management Report

Part 3 – Accounting
- Closing accounting entries, general closure and reopening of accounts
- Fixed assets – Depreciation, amortization and devaluation
- Financial Investments – Equity Method
- Inventories and work in progress – FIFO, LIFO and WACC

Part 4 - Fundamentals of financial statement analysis
- Reclassification of BS and IS
- Ratios
- Statement of Cash Flows – Direct and Indirect Method

Suggested readings:

Part 1 and 2: Tutino M. (2017), Bilancio e nuovi OIC, Cedam
Part 3: Paoloni M., Celli M. (2012), Introduzione alla contabilità generale, Cedam
Part 4: Paolucci G. (2016), Analisi di Bilancio, Hoepli

Slides and exercises available on the Professor's web page

The course addresses the following topics:

1. Theoretical models of public intervention: welfare economics; the new welfare economics; market failures;
2. The critical aspects of the new welfare economics;
3. Alternative approaches to welfare economics for collective decisions: the Musgrave model; the Lindahl model; the Johansen model; the Buchanan model;
4. The formation of collective decisions;
5. The theory of taxation;
6. Shifting and incidence of taxes;
7. The effects of taxes on choices between consumer goods, between work and leisure, between consumption and savings;
8. The excess burden of taxes;
9. Overview of the theory of optimal taxation.

1. for the general part, a text will be made available to students at the beginning of the course in pdf format;

2) for the section on the Italian tax system: Bosi P., Guerra M.C., I tributi nell'economia italiana, Il Mulino, Bologna, ed. 2023, capitoli III, IV, V, VI, VII, VIII

Main official statistical surveys: data production and interpretation. In particular: Consumer prices, Industrial production, Labour forces, Household consumptions, Income and living conditions, Household Income and Wealth. National accounts. Main statistical indicators for economic phenomena: (simple and complex) index numbers, measures of concentration.
Calendar adjusted and seasonal adjusted time series; chain-linked values. The use of moving averages to reconstruct the trend.
Introduction to econometrics. Single and multiple Linear Regression: ordinary least squares, goodness of fit, homoscedasticity and heteroscedasticity. Nonlinear regression functions. Regression with panel data. Regression with a binary dependent variable.
An introduction to the use of R for statistical analysis.

Class notes (in Italian) downloadable from the Moodle space of the course.
Press releases (Istat - Banca d'Italia).
Stock J.H. and Watson M.W., Introduction to Econometrics, Global edition, 4th Edition, 2020, Pearson.

NOTA BENE:
• Tutte le slides delle lezioni saranno rese disponibili, insieme a tutti gli altri materiali rilevanti, esclusivamente sulla piattaforma moodle del corso.

• I paragrafi da studiare dei capitoli di riferimento riportati tra parentesi verranno meglio indicati durante le lezioni e coincideranno con le parti che verranno trattate in aula e nelle slides.


Parte I – Economia Regionale
Testo di riferimento: Capello R. “Economia Regionale”, seconda edizione, Il Mulino.

Parti selezionate tratte da:

1. Introduzione: Economia e spazio (pag. 25-39)
2. Teorie della crescita regionale
a. Struttura produttiva e sviluppo (cap. IV)
b. La domanda (cap. V)
c. La dotazione fattoriale (cap. VI)
3. Teorie dello sviluppo locale
a. Competitività territoriale e sviluppo esogeno (cap. VII)
b. Competitività territoriale e sviluppo endogeno: le economie di agglomerazione (cap. VIII)
c. Competitività territoriale e sviluppo endogeno: le economie di agglomerazione (cap. IX)
4. Politica regionale Europea (materiali distribuiti durante le lezioni)


Parte II – Economia Industriale
Testo di riferimento: Lynne Pepall, Daniel J. Richards, George Norman e Giacomo Calzolari “Organizzazione Industriale” terza edizione, Mc Graw Hill Education

Parti selezionate tratte da:

1. Fondamenti di micro (solamente slides delle lezioni)
2. Oligopolio statico (capp. 8 e 9)
3. Ricerca e sviluppo e brevetti (cap.18)
4. Big data, piattaforme digitali e antitrust (articolo: G. Colangelo “Big data, piattaforme digitali e antitrust”, Mercato concorrenza regole/a. XVIII, n. 3, dicembre 2016)

Esercitazioni:
Durante l’orario di lezione sono previste esercitazioni pratiche che prevedono utilizzo e di banche dati ed elaborazioni

Testi di riferimento:
Capello R. “Economia Regionale”, seconda edizione, Il Mulino.
Lynne Pepall, Daniel J. Richards, George Norman e Giacomo Calzolari “Organizzazione Industriale” terza edizione, Mc Graw Hill Education

Part I: Linear algebra
The real n-dimensional vector space. Linear dependence and independence. Subspaces and spaces generated by vectors. Bases. Algebra of matrices. Determinant. Inverse matrix. Rank of a matrix. Systems of linear equations. Cramer's Theorem and Rouché-Capelli's Theorem. Homogeneous systems and linear dependence. Norm and Euclidean distance in . Scalar product. Sequences in . Topology and metrics in . Eigenvalues and eigenvectors. Diagonalization of matrices. Properties of eigenvalues.
Part II: Calculus of functions of several variables:
Continuous functions and Weierstrass theorem. Concave or convex functions. Partial derivatives and gradient. Differential. Derivations along a curve and directional derivative. Second order derivatives. Schwarz's theorem. Hessian matrix. Implicit function thoerem. Comparative statics. Inverse function theorem. Quadratic forms and matrices. Sign of a quadratic form.
Part III: Optimization:
Local and global maximum or minimum. First order conditions and second order conditions for free optimization. Equality constraints. Inequality constraints. Substitution method. Lagrange multiplier theorem. Second order conditions with constraints. Optimization for convex functions. Economic applications.
Part IV: Ordinary differential equations and systems
Definitions and examples. Exact differential. Equations in separable variables. Exact equations. Homogeneous equations. Malthusian growth model. Logistic growth model. Second order linear differential equations. General theorem of existence and uniqueness of the solution. Field of directions. Economic applications. Two-dimensional differential equation systems. Systems of linear differential equations: resolving method using eigenvalues, stationary states and their stability. Economic applications.

Simon & Blume: “Matematica per le scienze economiche” ed. Egea.
Other materials will be available in the course Moodle class

Other Textbooks:
Mastroeni L. and Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.

PARTE GENERALE
- Nozioni introduttive: la norma e l’ordinamento giuridico. Le fonti del diritto e i conflitti tra le stesse. Il diritto privato. L’interpretazione della legge e l’analogia.
- Le situazioni giuridiche soggettive e i rapporti giuridici.
- Il soggetto del rapporto giuridico: persone fisiche e persone giuridiche. I diritti della personalità.
- L’oggetto del rapporto giuridico: i beni. I diritti reali: proprietà, possesso, diritti reali di godimento. Comunione e condominio. L’usucapione.
- Il rapporto obbligatorio: adempimento, inadempimento, vicende dell’obbligazione, tipologie di obbligazioni, tutela del credito e garanzie dell’obbligazione.
- Atto, fatto e negozio giuridico. Il contratto: il contratto in generale, formazione e vicende del contratto, le patologie, i singoli contratti nominati.
- I fatti illeciti e le altre fonti delle obbligazioni.
- La tutela dei diritti: la trascrizione. I diritti reali di garanzia, le azioni a difesa della garanzia patrimoniale, la prescrizione e la decadenza.
PARTE SPECIALE
- Diritti e tutele delle persone minori di età

FUNDAMENTAL/GENERAL PART
One of the following Manuals, alternative to each other, as long as they are updated to the latest edition:
- S. MAZZAMUTO (a cura di), Manuale di diritto privato, Giappichelli, Torino, ult. ed, (Parte I, II (excluded cap. V), parte V, VI, VII, VIII)
- L. NIVARRA, V. RICCIUTO, C. SCOGNAMIGLIO, Istituzioni di diritto privato, Torino, ult. ed. (excluded cap. XIII e XIV)
- P. PERLINGIERI, Istituzioni di diritto civile, Edizioni Scientifiche Italiane, Napoli, ult. ed. (excluded parte VI, VII e VIII)
- A. TORRENTE e P. SCHLESINGER, Manuale di diritto privato, Giuffré, Milano, ult. ed. (until cap. LV; excluded cap. LII e LIII)

SPECIAL PART
ETTORE BATTELLI, Diritto privato delle persone minori di età, Giappichelli, Torino, 2021 (p.1-155).

To follow the lessons, it is essential:
A. DI MAJO (eds), Codice Civile, Giuffrè, Milano, last edition.
G. PERLINGIERI e M. ANGELONE (a cura di), Codice civile, ESI, Napoli, last edition

1. Concepts, Issues
2. Welfare economics
3. Redistributive policies
4. Imperfect competition, externalities, industrial policy, regional policies
5. Labour market policies
6. Fiscal Policy
7. Monetary Policy
8. Financial Stability
9. Macroeconomic policies in an open economy
10. Growth Policies

R Cellini, Politica Economica, McGraw Hill, 2019

1. Introduction: the characteristics of the field of study and the specificities of "Business Organization"
2. The organizational literature: an outline of the history of organizational thought
3. The organizational design choices (organizational design): the levels of analysis and intervention
4. Work design choices
4.1 A theoretical study: the analysis and discussion of the theory of the Scientific Management by Frederick Taylor
4.2 The reassembly of the divided work: the job redesign approach and the socio-technical approach
4.3 The post-Fordist approaches: Human Relation; Human Resource; socio-technical approach
4.4 The new forms of work organization: Industry 4.0 and Flexible work arrangements
5. Human Resources Management
5.1 Phases, activities and methodologies
5.2 Actors of the HRM
5.3 The analysis of positions: tools and methods adopted in business practice
6. Work process design choices (inter-organizational relations): post-Fordism solutions and organizational techniques
7. Design choices of the organizational structure (business structure)
7.1 The problem of choosing the "formal configuration" of the organization: the origins of the topic in the literature
7.2 Traditional organizational structures: the functional structure, the divisional structure (the M form), the matrix structure.
7.3 The "post-Fordist" organizational structures: the process structure, the modular structure, the internal network.
7.4 Business groups and Holding companies8. Design choices of organizational boundaries
8.1 The problem of the "boundaries" of the firm: origins and evolution of the literature on the subject
8.2 Outsourcing choices
8.3. Alliances and collaboration agreements between companies (motivations and contractual forms)
8.4 Business networks (outline)

The textbook is under revision. Additional readings will be posted online at the beginning of the course

1. Introduction: the characteristics of the field of study and the specificities of "Business Organization"

2. The organizational literature: an outline of the history of organizational thought

3. The organizational design choices (organizational design): the levels of analysis and intervention

4. Decisions about for work design A theoretical study: the analysis and discussion of the theory of the Scientific Management by Frederick Taylor
4.2 The reassembly of the divided work: the job redesign approach and the socio-technical approach
4.3 The post-Fordist approaches: Human Relation; Human Resource; socio-technical approach
4.4 The new forms of work organization: Industry 4.0 and Flexible work arrangements

5. Human Resources Management
5.1 Phases, activities and methodologies
5.2 Actors of the HRM
5.3 The analysis of positions: tools and methods adopted in business practice

6. Work process design choices (inter-organizational relations): post-Fordism solutions and organizational techniques

7. Design choices of the organizational structure (business structure)
7.1 The problem of choosing the "formal configuration" of the organization: the origins of the topic in the literature
7.2 Traditional organizational structures: the functional structure, the divisional structure (the M form), the matrix structure.
7.3 The "post-Fordist" organizational structures: the process structure, the modular structure, the internal network.
7.4 Business groups and Holding companies

8. Design choices of organizational boundaries
8.1 The problem of the "boundaries" of the firm: origins and evolution of the literature on the subject
8.2 Outsourcing choices
8.3. Alliances and collaboration agreements between companies (motivations and contractual forms)
8.4 Business networks (outline)

Decastri M. (2016) Leggere le organizzazioni. Le teorie e i modelli per capire. Manuale di organizzazione aziendale
Textbook provided by the instructor

The course consists of two teaching modules.
The first module concerns the general part and trade union law (Introduction to the study of labor law). The boundaries and the meaning of labor law. Historical evolution and current trends. Sources. Constitutional principles. European sources and international aspects of Trade union law. Trade union freedom and Trade Union Organization. Union rights and their protection with particular reference to art. 28 of the Workers’ Statute. The collective agreement: the structure of collective bargaining, the negotiability and effectiveness of the collective agreements at different levels, the relationship between law and collective agreement. The strike and other forms of union struggle; the strike in essential public services.
The second module concerns the employment relationship: the employment contracts (subordinate, autonomous, coordinated). The flexible contractual forms. The forms of indirect acquisition of work. The subordinate employment contract: the subjective and objective requirements. The obligations of the employer: collaboration, diligence, obedience, loyalty. The powers of the employer. The protection of the person, of dignity and freedom of workers. The prohibitions of discrimination. Worker’s rights: pay, holidays, rest, leave, right to health and safety. The content of the work performance: the tasks, the working hours. The end of the employment relationship: individual dismissals. The enterprise crisis and excess staff: earning redundancy fund, solidarity contracts, transfer of the undertaking, collective dismissals. The protection of the employer’s rights; waivers and transactions; limitation. The employment services and the worker’s protection on the labor market.

M. Esposito, L. Gaeta, A. Zoppoli, L. Zoppoli, Diritto del lavoro e sindacale, Giappichelli, 2023

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
First Part: BUSINESS ADMINISTRATION
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identities. Types of firms.
2) The firm in its economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and profitability. Information Systems Governance and Internal controls (overview). Planning in business (overview).
Second Parte: ACCRUAL ACCOUNTING
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

First Part: Business Administration
Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2° edizione, 2021
Onida, P., Economia d'azienda, Utet, Torino, 1970
Zanda, G., Lineamenti di Economia Aziendale, Edizioni Kappa, Roma, 2006

Second Part: Accrual Accounting
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2° edizione, 2020
For business administration and accounting exercises:
Paoloni M. (a cura di), Mattei G., Paoloni, N., Eserciziario di economia aziendale e contabilità, CEDAM, 2018

Syllabus
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Robert N. Anthony – Leslie K. Breitner, Essentials of Accounting, Prentice Hall, 2007
Slides/teaching notes will be available on the website

Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.
Limits:
Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Integral calculus:
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

Suggested materials:
- Notes can be downloaded online from the course Matematica Generale on Moodle at the website: https://economia.el.uniroma3.it/
Optional materials:
- Loretta Mastroeni, Alessandro Mazzoccoli, Pierluigi Vellucci. Esercizi di matematica generale. Esculapio, 2023

Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.

Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.

Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.

Real functions of a real variable:

Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.

Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.

Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).

Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).

Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.

Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.

Linear algebra:

Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.

Integral calculus:

Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(w.p.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.

(w.p.) = “with proof”

Suggested materials:

- Mastroeni, Mazzoccoli, Vellucci: "Esercizi di matematica generale". Società editrice Esculapio. ISBN 9788893853910

Optional materials:

-Peccati, Salsa, Squellati. "Matematica per l'economia e l'azienda". Egea.

-Bramanti, Pagani, Salsa. Calcolo infinitesimale e algebra lineare Seconda edizione

- Alberto Bersani, Francesco Manzini, Loretta Mastroeni. Esercizi di Matematica Generale: Per i corsi del nuovo ordinamento delle Facoltà di Economia. Società Editrice Esculapio, 2009.

1. National accounting system: basic defintions and identities. Main macroeconomic indicators
2. Keynes’s theory: aggregate demand and equilibrium output
3. Keynes’s theory: money and interest
4. The IS-LM model
5. The AS-AD model
6. Inflation and unemployment
7. Macroeconomics of the European Union
8. Money: creation and control

Compulsory material:
1) Textbook: Antonella Stirati, Fondamenti di macroeconomia, Giappichelli, ISBN 9791221108514 (forthcoming in September 2024. Check the detailed programme for precise indications on the parts of the textbook to be studied). Students may ask for alternative material in English. Please contact prof Palumbo
2) Additional teaching material (lecture notes, slides, etc, made available on the moodle website)

The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

Fondamenti di Macroeconomia, elementi di base, di Antonella Stirati; Giappichelli 2024

Introduction to computer science
Computer architecture
CPU, main memory, secondary memory, input/output peripherals
The operating system and application software
Overview of text document editors
Creating and managing text documents
Tools for formatting text, images, tables, and styles in text documents
Review capabilities of a text document
Advanced features for text documents
Spreadsheet overview
Cells, formulas and major spreadsheet features
Using functions and constructing charts in spreadsheets
Advanced features for spreadsheets

Materials provided by the lecturer

The program includes:
Introduction to law
Forms of State and forms of Government
Beyond the State: the EU
The sources of law
Parliament and its functions
Institutes of direct democracy
The abrogative referendum.
The Government and its functions
The President of the Republic and his attributions
Principles on the subject of Administration
The other organs
Local ordering
Rights and freedom
The economic Constitution
Judicial power
Constitutional Justice

It is recommended the study of one of the following books:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, latest edition
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, latest edition
F. Modugno (a cura di), Diritto Pubblico, Torino, Giappichelli, latest edition
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, latest edition

The Public Law course is divided into two modules.
Module I covers the following topics: theory of social groups; the normative social groups; the structure of the legal system; power and its species; power-sharing techniques; the forms of exercise of power: the legal norm and the provision; subjects; interests; the goods; subjective legal situations; the legal facts; human behaviors; the legal effects; the responsability; the regulatory levels of government (international, European Community, state, local); the organization of public authorities; public functions (political direction, regulation, administration, jurisdiction).
The II Module deals with the Italian legal system and the regulatory principles of its political, legislative, administrative and jurisdictional activity.

For preparation for Modules I and II we recommend studying a manual chosen from the following:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, ult. ed.
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, ult. ed.
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, ult. ed.

Detailed program by chapters.
Part 1. Introduction
Chapter 1. Thinking as an economist (all)
Chapter 2. Supply and Demand (All)
Part 2. Consumer theory.
Chapter 3. Rational consumer choice (all but par. 3.5)
Chapter 4. The utility function (all except par. 4.6.4)
Chapter 5. The applications of rational choice and demand: paragraphs 5.4 and 5.4.1 only.
Part 3. Business theory and market structure.
Chapter 9. Production (all). Appendix to Chapter 9: A.9.1, A.9.2, A.9.2 only
Chapter 10. Costs (all except Section 10.7)
Chapter 11. Perfect competition (all except 11.11.1, 11.12.1, 11.12.2, 11.12.3, 11.14)
Chapter 12. Monopoly (all but paragraph 12.9)

R.H. Frank e E. Cartwright (2021) Microeconomia, VIII edizione. Milano: McGraw-Hill

Elements of the theory of production
- inputs, outputs and production methods
- the subsistence economy
- the economy with a surplus
The surplus approach to commodity value and income distribution
- the relevance of social and institutional elements to income distribution
- the explanation of the real wage rate
- the "core" of the classical approach
- the link between profit rate and relative prices
- the price equations
- the classical theory of rent
The theory of consumer choice
- budget set and budget constraint
- preferences
- consumer choice
- consumer-good demand curves
The theory of firm choice
- the function of production
- profit maximisation
- isoquants and isocosts
- the output expansion path and long-term cost curves
Production factors and the marginalist explanation of income distribution
- marginal and average productivity of factors
- the demand curves of factors of production
- equilibrium between supply and demand for factors of production
Market forms
- perfect competition
- monopoly
- Cournot oligopoly
- Stackelberg oligopoly
Introduction to the welfare economics
- allocations and Edgeworth box
- Pareto improvements and Pareto optima
- first theorem of welfare economics

i) “Elementi di teoria della produzione”, Dispensa n. 1 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
ii) “La teoria classica della distribuzione e dei prezzi relativi”, Dispensa n. 2 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
iii) “Teoria marginalista della distribuzione”, Dispensa n. 3 (materiale didattico redatto da S.M. Fratini).
iv) Frank Robert H.; Cartwright Edward; Piras R. Microeconomia. McGraw-Hill Libri Italia, Milano. 2021.
v) “Glossario ed Esercizi Svolti di Microeconomia” (materiale didattico redatto da S.M. Fratini e D. Pignalosa).

An introduction to the fundamental ideas of statistics. Topics include:

Descriptive statistics: graphical summaries of data, measuring the center of quantitative data (mode, median, mean), measuring the variability of quantitative data (standard deviation, variance), simmetry of a distribution (Fisher coefficient), the association between two variables (chi-square), the association between two quantitative variables (covariance, correlation coefficient).

Probability: probability of events (probability of the complement of an event, of the union and intersection of two events, conditional probability, independent events, Bayes theorem), discrete and continuous random variables (the Bernoully r.v., the Binomial r.v., the Poisson r.v., the Normal r.v., the Student t r.v., che Chi-square r.v.).

Inferential statistics: sample versus population, sampling distributions, point and interval estimates of population parameters, confidence intervals for a population mean and a proportion, significance tests about hypotheses on a population mean and a proportion, p-values.

Regression analysis: the regression line, ordinary least squares, describing the strength of the association, nonlinear regression models, confidence intervals and tests on the parameters of the regression line, prediction.

G.Cicchitelli, P.D'Urso, M.Minozzo. Statistica: principi e metodi. Pearson, fourth edition:
Chap. 1 (excluding 1.11), Chap. 2 (excluding 2.4, 2.5), Chap. 3 (excluding 3.4, 3.5, 3.6), Chap. 4 (excluding 4.3, 4.4, 4.5, 4.6, 4.15), Chap. 5 (excluding 5.3, 5.6, 5.7, 5.8), Chap. 6 (excluding 6.3), Chap. 9 (excluding 9.3), Chap. 10, Chap. 11 (excluding 11.2.1), Chap. 12, Chap. 13, Chap. 14 (excluding 14.2, 14.6, 14.7),Chap. 17 (excluding 17.6), Chap.18 (excluding 18.3, 18.4), Chap. 19 (excluding 19.5), Chap. 20 (excluding 20.6, 20.7), Chap. 22 (excluding 22.2.2), Chap. 23.

A collection of exercises by the teacher is available to students on Moodle.

Descriptive statistics:
variables and their measurement, univariate distributions, describing data with tables and graphs, measures of position, variability.
Bivariate descriptive statistics: independence, association, correlation, probability distributions for discrete and continuous variables, sampling distributions
Inference: estimation, hypothesis test, regression

A. Agresti, B. Finlay. Statistical methods for the social sciences. Pearson International Edition-4th edition (2009)

Part 1 - The theory of Financial Statements
-Introduction to the study of the Financial Statements
- The basic functions of the Financial Statements
- The nature of income and capital
- The purposes of the Financial Statements
- The relationship between income, evaluation criteria and purposes of the Financial Statements
- The goals of the Financial Statements in corporate doctrine: the "alpha" goal and the "beta" goal

Part 2 - The Financial Statements according to the Civil Code
- The Financial Statement documents - Structure and content (Articles 2423-ter - 2425 of the Italian Civil Code)
- The general clause and the principles for preparing the Financial Statements (articles 2423 - 2423-bis of the Italian Civil Code)
- The specific evaluation criteria (art. 2426 of the civil code)
- Fixed assets
- Receivables
- Inventories (Lifo, Fifo, Cmp)
- Work in progress assets
- The content of the Notes and the Management Report

Part 3 – Accounting
- Closing accounting entries, general closure and reopening of accounts
- Fixed assets – Depreciation, amortization and devaluation
- Financial Investments – Equity Method
- Inventories and work in progress – FIFO, LIFO and WACC

Part 4 - Fundamentals of financial statement analysis
- Reclassification of BS and IS
- Ratios
- Statement of Cash Flows – Direct and Indirect Method

Suggested readings:

Part 1 and 2: Tutino M. (2017), Bilancio e nuovi OIC, Cedam
Part 3: Paoloni M., Celli M. (2012), Introduzione alla contabilità generale, Cedam
Part 4: Paolucci G. (2016), Analisi di Bilancio, Hoepli

Slides and exercises available on the Professor's web page

The course addresses the following topics:

1. Theoretical models of public intervention: welfare economics; the new welfare economics; market failures;
2. The critical aspects of the new welfare economics;
3. Alternative approaches to welfare economics for collective decisions: the Musgrave model; the Lindahl model; the Johansen model; the Buchanan model;
4. The formation of collective decisions;
5. The theory of taxation;
6. Shifting and incidence of taxes;
7. The effects of taxes on choices between consumer goods, between work and leisure, between consumption and savings;
8. The excess burden of taxes;
9. Overview of the theory of optimal taxation.

1. for the general part, a text will be made available to students at the beginning of the course in pdf format;

2) for the section on the Italian tax system: Bosi P., Guerra M.C., I tributi nell'economia italiana, Il Mulino, Bologna, ed. 2023, capitoli III, IV, V, VI, VII, VIII

PARTE GENERALE
- Nozioni introduttive: la norma e l’ordinamento giuridico. Le fonti del diritto e i conflitti tra le stesse. Il diritto privato. L’interpretazione della legge e l’analogia.
- Le situazioni giuridiche soggettive e i rapporti giuridici.
- Il soggetto del rapporto giuridico: persone fisiche e persone giuridiche. I diritti della personalità.
- L’oggetto del rapporto giuridico: i beni. I diritti reali: proprietà, possesso, diritti reali di godimento. Comunione e condominio. L’usucapione.
- Il rapporto obbligatorio: adempimento, inadempimento, vicende dell’obbligazione, tipologie di obbligazioni, tutela del credito e garanzie dell’obbligazione.
- Atto, fatto e negozio giuridico. Il contratto: il contratto in generale, formazione e vicende del contratto, le patologie, i singoli contratti nominati.
- I fatti illeciti e le altre fonti delle obbligazioni.
- La tutela dei diritti: la trascrizione. I diritti reali di garanzia, le azioni a difesa della garanzia patrimoniale, la prescrizione e la decadenza.
PARTE SPECIALE
- Diritti e tutele delle persone minori di età

FUNDAMENTAL/GENERAL PART
One of the following Manuals, alternative to each other, as long as they are updated to the latest edition:
- S. MAZZAMUTO (a cura di), Manuale di diritto privato, Giappichelli, Torino, ult. ed, (Parte I, II (excluded cap. V), parte V, VI, VII, VIII)
- L. NIVARRA, V. RICCIUTO, C. SCOGNAMIGLIO, Istituzioni di diritto privato, Torino, ult. ed. (excluded cap. XIII e XIV)
- P. PERLINGIERI, Istituzioni di diritto civile, Edizioni Scientifiche Italiane, Napoli, ult. ed. (excluded parte VI, VII e VIII)
- A. TORRENTE e P. SCHLESINGER, Manuale di diritto privato, Giuffré, Milano, ult. ed. (until cap. LV; excluded cap. LII e LIII)

SPECIAL PART
ETTORE BATTELLI, Diritto privato delle persone minori di età, Giappichelli, Torino, 2021 (p.1-155).

To follow the lessons, it is essential:
A. DI MAJO (eds), Codice Civile, Giuffrè, Milano, last edition.
G. PERLINGIERI e M. ANGELONE (a cura di), Codice civile, ESI, Napoli, last edition

- The company and the entrepreneur: essential notions and characteristics.

- The various types and forms of enterprise.

- The entrepreneur's auxiliaries.

- The company: notion and characters.

- The circulation of the company.

- Distinguishing marks.

- Discipline of unfair competition.

- Competition rules: Antitrust Law.

- Companies: general concept, partnership contract, essential characteristics.

- Various types of companies: partnerships ("società di persone") and capital companies ("società di capitali").

- Dissolution, transformation, merger and demerger.

- Groups of companies.

- Cooperative societies.

- Consortia and consortium companies.

- Commercial contracts.

- General profiles of credit instruments.

- Bills of exchange, bank cheques, cashier's cheques and other securities.

- The crisis of the company.

Ask the Professor for English lectures.

- The company and the entrepreneur: essential notions and characteristics.

- The various types and forms of enterprise.

- The entrepreneur's auxiliaries.

- The company: notion and characters.

- The circulation of the company.

- Distinguishing marks.

- Discipline of unfair competition.

- Competition rules: Antitrust Law.

- Companies: general concept, partnership contract, essential characteristics.

- Various types of companies: partnerships ("società di persone") and capital companies ("società di capitali").

- Dissolution, transformation, merger and demerger.

- Groups of companies.

- Cooperative societies.

- Consortia and consortium companies.

- Commercial contracts.

- General profiles of credit instruments.

- Bills of exchange, bank cheques, cashier's cheques and other securities.

- The crisis of the company.

Ask the Professor for English lectures.

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
First Part: BUSINESS ADMINISTRATION
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identities. Types of firms.
2) The firm in its economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and profitability. Information Systems Governance and Internal controls (overview). Planning in business (overview).
Second Parte: ACCRUAL ACCOUNTING
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

First Part: Business Administration
Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2° edizione, 2021
Onida, P., Economia d'azienda, Utet, Torino, 1970
Zanda, G., Lineamenti di Economia Aziendale, Edizioni Kappa, Roma, 2006

Second Part: Accrual Accounting
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2° edizione, 2020
For business administration and accounting exercises:
Paoloni M. (a cura di), Mattei G., Paoloni, N., Eserciziario di economia aziendale e contabilità, CEDAM, 2018

Syllabus
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Robert N. Anthony – Leslie K. Breitner, Essentials of Accounting, Prentice Hall, 2007
Slides/teaching notes will be available on the website

1. National accounting system: basic defintions and identities. Main macroeconomic indicators
2. Keynes’s theory: aggregate demand and equilibrium output
3. Keynes’s theory: money and interest
4. The IS-LM model
5. The AS-AD model
6. Inflation and unemployment
7. Macroeconomics of the European Union
8. Money: creation and control

Compulsory material:
1) Textbook: Antonella Stirati, Fondamenti di macroeconomia, Giappichelli, ISBN 9791221108514 (forthcoming in September 2024. Check the detailed programme for precise indications on the parts of the textbook to be studied). Students may ask for alternative material in English. Please contact prof Palumbo
2) Additional teaching material (lecture notes, slides, etc, made available on the moodle website)

The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

Fondamenti di Macroeconomia, elementi di base, di Antonella Stirati; Giappichelli 2024

Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.
Limits:
Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Integral calculus:
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

Suggested materials:
- Notes can be downloaded online from the course Matematica Generale on Moodle at the website: https://economia.el.uniroma3.it/
Optional materials:
- Loretta Mastroeni, Alessandro Mazzoccoli, Pierluigi Vellucci. Esercizi di matematica generale. Esculapio, 2023

Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.

Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.

Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.

Real functions of a real variable:

Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.

Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.

Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).

Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).

Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.

Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.

Linear algebra:

Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.

Integral calculus:

Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(w.p.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.

(w.p.) = “with proof”

Suggested materials:

- Mastroeni, Mazzoccoli, Vellucci: "Esercizi di matematica generale". Società editrice Esculapio. ISBN 9788893853910

Optional materials:

-Peccati, Salsa, Squellati. "Matematica per l'economia e l'azienda". Egea.

-Bramanti, Pagani, Salsa. Calcolo infinitesimale e algebra lineare Seconda edizione

- Alberto Bersani, Francesco Manzini, Loretta Mastroeni. Esercizi di Matematica Generale: Per i corsi del nuovo ordinamento delle Facoltà di Economia. Società Editrice Esculapio, 2009.

Introduction to computer science
Computer architecture
CPU, main memory, secondary memory, input/output peripherals
The operating system and application software
Overview of text document editors
Creating and managing text documents
Tools for formatting text, images, tables, and styles in text documents
Review capabilities of a text document
Advanced features for text documents
Spreadsheet overview
Cells, formulas and major spreadsheet features
Using functions and constructing charts in spreadsheets
Advanced features for spreadsheets

Materials provided by the lecturer

The program includes:
Introduction to law
Forms of State and forms of Government
Beyond the State: the EU
The sources of law
Parliament and its functions
Institutes of direct democracy
The abrogative referendum.
The Government and its functions
The President of the Republic and his attributions
Principles on the subject of Administration
The other organs
Local ordering
Rights and freedom
The economic Constitution
Judicial power
Constitutional Justice

It is recommended the study of one of the following books:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, latest edition
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, latest edition
F. Modugno (a cura di), Diritto Pubblico, Torino, Giappichelli, latest edition
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, latest edition

The Public Law course is divided into two modules.
Module I covers the following topics: theory of social groups; the normative social groups; the structure of the legal system; power and its species; power-sharing techniques; the forms of exercise of power: the legal norm and the provision; subjects; interests; the goods; subjective legal situations; the legal facts; human behaviors; the legal effects; the responsability; the regulatory levels of government (international, European Community, state, local); the organization of public authorities; public functions (political direction, regulation, administration, jurisdiction).
The II Module deals with the Italian legal system and the regulatory principles of its political, legislative, administrative and jurisdictional activity.

For preparation for Modules I and II we recommend studying a manual chosen from the following:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, ult. ed.
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, ult. ed.
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, ult. ed.

Detailed program by chapters.
Part 1. Introduction
Chapter 1. Thinking as an economist (all)
Chapter 2. Supply and Demand (All)
Part 2. Consumer theory.
Chapter 3. Rational consumer choice (all but par. 3.5)
Chapter 4. The utility function (all except par. 4.6.4)
Chapter 5. The applications of rational choice and demand: paragraphs 5.4 and 5.4.1 only.
Part 3. Business theory and market structure.
Chapter 9. Production (all). Appendix to Chapter 9: A.9.1, A.9.2, A.9.2 only
Chapter 10. Costs (all except Section 10.7)
Chapter 11. Perfect competition (all except 11.11.1, 11.12.1, 11.12.2, 11.12.3, 11.14)
Chapter 12. Monopoly (all but paragraph 12.9)

R.H. Frank e E. Cartwright (2021) Microeconomia, VIII edizione. Milano: McGraw-Hill

Elements of the theory of production
- inputs, outputs and production methods
- the subsistence economy
- the economy with a surplus
The surplus approach to commodity value and income distribution
- the relevance of social and institutional elements to income distribution
- the explanation of the real wage rate
- the "core" of the classical approach
- the link between profit rate and relative prices
- the price equations
- the classical theory of rent
The theory of consumer choice
- budget set and budget constraint
- preferences
- consumer choice
- consumer-good demand curves
The theory of firm choice
- the function of production
- profit maximisation
- isoquants and isocosts
- the output expansion path and long-term cost curves
Production factors and the marginalist explanation of income distribution
- marginal and average productivity of factors
- the demand curves of factors of production
- equilibrium between supply and demand for factors of production
Market forms
- perfect competition
- monopoly
- Cournot oligopoly
- Stackelberg oligopoly
Introduction to the welfare economics
- allocations and Edgeworth box
- Pareto improvements and Pareto optima
- first theorem of welfare economics

i) “Elementi di teoria della produzione”, Dispensa n. 1 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
ii) “La teoria classica della distribuzione e dei prezzi relativi”, Dispensa n. 2 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
iii) “Teoria marginalista della distribuzione”, Dispensa n. 3 (materiale didattico redatto da S.M. Fratini).
iv) Frank Robert H.; Cartwright Edward; Piras R. Microeconomia. McGraw-Hill Libri Italia, Milano. 2021.
v) “Glossario ed Esercizi Svolti di Microeconomia” (materiale didattico redatto da S.M. Fratini e D. Pignalosa).

An introduction to the fundamental ideas of statistics. Topics include:

Descriptive statistics: graphical summaries of data, measuring the center of quantitative data (mode, median, mean), measuring the variability of quantitative data (standard deviation, variance), simmetry of a distribution (Fisher coefficient), the association between two variables (chi-square), the association between two quantitative variables (covariance, correlation coefficient).

Probability: probability of events (probability of the complement of an event, of the union and intersection of two events, conditional probability, independent events, Bayes theorem), discrete and continuous random variables (the Bernoully r.v., the Binomial r.v., the Poisson r.v., the Normal r.v., the Student t r.v., che Chi-square r.v.).

Inferential statistics: sample versus population, sampling distributions, point and interval estimates of population parameters, confidence intervals for a population mean and a proportion, significance tests about hypotheses on a population mean and a proportion, p-values.

Regression analysis: the regression line, ordinary least squares, describing the strength of the association, nonlinear regression models, confidence intervals and tests on the parameters of the regression line, prediction.

G.Cicchitelli, P.D'Urso, M.Minozzo. Statistica: principi e metodi. Pearson, fourth edition:
Chap. 1 (excluding 1.11), Chap. 2 (excluding 2.4, 2.5), Chap. 3 (excluding 3.4, 3.5, 3.6), Chap. 4 (excluding 4.3, 4.4, 4.5, 4.6, 4.15), Chap. 5 (excluding 5.3, 5.6, 5.7, 5.8), Chap. 6 (excluding 6.3), Chap. 9 (excluding 9.3), Chap. 10, Chap. 11 (excluding 11.2.1), Chap. 12, Chap. 13, Chap. 14 (excluding 14.2, 14.6, 14.7),Chap. 17 (excluding 17.6), Chap.18 (excluding 18.3, 18.4), Chap. 19 (excluding 19.5), Chap. 20 (excluding 20.6, 20.7), Chap. 22 (excluding 22.2.2), Chap. 23.

A collection of exercises by the teacher is available to students on Moodle.

Descriptive statistics:
variables and their measurement, univariate distributions, describing data with tables and graphs, measures of position, variability.
Bivariate descriptive statistics: independence, association, correlation, probability distributions for discrete and continuous variables, sampling distributions
Inference: estimation, hypothesis test, regression

A. Agresti, B. Finlay. Statistical methods for the social sciences. Pearson International Edition-4th edition (2009)

Part 1 - The theory of Financial Statements
-Introduction to the study of the Financial Statements
- The basic functions of the Financial Statements
- The nature of income and capital
- The purposes of the Financial Statements
- The relationship between income, evaluation criteria and purposes of the Financial Statements
- The goals of the Financial Statements in corporate doctrine: the "alpha" goal and the "beta" goal

Part 2 - The Financial Statements according to the Civil Code
- The Financial Statement documents - Structure and content (Articles 2423-ter - 2425 of the Italian Civil Code)
- The general clause and the principles for preparing the Financial Statements (articles 2423 - 2423-bis of the Italian Civil Code)
- The specific evaluation criteria (art. 2426 of the civil code)
- Fixed assets
- Receivables
- Inventories (Lifo, Fifo, Cmp)
- Work in progress assets
- The content of the Notes and the Management Report

Part 3 – Accounting
- Closing accounting entries, general closure and reopening of accounts
- Fixed assets – Depreciation, amortization and devaluation
- Financial Investments – Equity Method
- Inventories and work in progress – FIFO, LIFO and WACC

Part 4 - Fundamentals of financial statement analysis
- Reclassification of BS and IS
- Ratios
- Statement of Cash Flows – Direct and Indirect Method

Suggested readings:

Part 1 and 2: Tutino M. (2017), Bilancio e nuovi OIC, Cedam
Part 3: Paoloni M., Celli M. (2012), Introduzione alla contabilità generale, Cedam
Part 4: Paolucci G. (2016), Analisi di Bilancio, Hoepli

Slides and exercises available on the Professor's web page

The course addresses the following topics:

1. Theoretical models of public intervention: welfare economics; the new welfare economics; market failures;
2. The critical aspects of the new welfare economics;
3. Alternative approaches to welfare economics for collective decisions: the Musgrave model; the Lindahl model; the Johansen model; the Buchanan model;
4. The formation of collective decisions;
5. The theory of taxation;
6. Shifting and incidence of taxes;
7. The effects of taxes on choices between consumer goods, between work and leisure, between consumption and savings;
8. The excess burden of taxes;
9. Overview of the theory of optimal taxation.

1. for the general part, a text will be made available to students at the beginning of the course in pdf format;

2) for the section on the Italian tax system: Bosi P., Guerra M.C., I tributi nell'economia italiana, Il Mulino, Bologna, ed. 2023, capitoli III, IV, V, VI, VII, VIII

Main official statistical surveys: data production and interpretation. In particular: Consumer prices, Industrial production, Labour forces, Household consumptions, Income and living conditions, Household Income and Wealth. National accounts. Main statistical indicators for economic phenomena: (simple and complex) index numbers, measures of concentration.
Calendar adjusted and seasonal adjusted time series; chain-linked values. The use of moving averages to reconstruct the trend.
Introduction to econometrics. Single and multiple Linear Regression: ordinary least squares, goodness of fit, homoscedasticity and heteroscedasticity. Nonlinear regression functions. Regression with panel data. Regression with a binary dependent variable.
An introduction to the use of R for statistical analysis.

Class notes (in Italian) downloadable from the Moodle space of the course.
Press releases (Istat - Banca d'Italia).
Stock J.H. and Watson M.W., Introduction to Econometrics, Global edition, 4th Edition, 2020, Pearson.

PARTE GENERALE
- Nozioni introduttive: la norma e l’ordinamento giuridico. Le fonti del diritto e i conflitti tra le stesse. Il diritto privato. L’interpretazione della legge e l’analogia.
- Le situazioni giuridiche soggettive e i rapporti giuridici.
- Il soggetto del rapporto giuridico: persone fisiche e persone giuridiche. I diritti della personalità.
- L’oggetto del rapporto giuridico: i beni. I diritti reali: proprietà, possesso, diritti reali di godimento. Comunione e condominio. L’usucapione.
- Il rapporto obbligatorio: adempimento, inadempimento, vicende dell’obbligazione, tipologie di obbligazioni, tutela del credito e garanzie dell’obbligazione.
- Atto, fatto e negozio giuridico. Il contratto: il contratto in generale, formazione e vicende del contratto, le patologie, i singoli contratti nominati.
- I fatti illeciti e le altre fonti delle obbligazioni.
- La tutela dei diritti: la trascrizione. I diritti reali di garanzia, le azioni a difesa della garanzia patrimoniale, la prescrizione e la decadenza.
PARTE SPECIALE
- Diritti e tutele delle persone minori di età

FUNDAMENTAL/GENERAL PART
One of the following Manuals, alternative to each other, as long as they are updated to the latest edition:
- S. MAZZAMUTO (a cura di), Manuale di diritto privato, Giappichelli, Torino, ult. ed, (Parte I, II (excluded cap. V), parte V, VI, VII, VIII)
- L. NIVARRA, V. RICCIUTO, C. SCOGNAMIGLIO, Istituzioni di diritto privato, Torino, ult. ed. (excluded cap. XIII e XIV)
- P. PERLINGIERI, Istituzioni di diritto civile, Edizioni Scientifiche Italiane, Napoli, ult. ed. (excluded parte VI, VII e VIII)
- A. TORRENTE e P. SCHLESINGER, Manuale di diritto privato, Giuffré, Milano, ult. ed. (until cap. LV; excluded cap. LII e LIII)

SPECIAL PART
ETTORE BATTELLI, Diritto privato delle persone minori di età, Giappichelli, Torino, 2021 (p.1-155).

To follow the lessons, it is essential:
A. DI MAJO (eds), Codice Civile, Giuffrè, Milano, last edition.
G. PERLINGIERI e M. ANGELONE (a cura di), Codice civile, ESI, Napoli, last edition

Part I: Linear algebra
The real n-dimensional vector space. Linear dependence and independence. Subspaces and spaces generated by vectors. Bases. Algebra of matrices. Determinant. Inverse matrix. Rank of a matrix. Systems of linear equations. Cramer's Theorem and Rouché-Capelli's Theorem. Homogeneous systems and linear dependence. Norm and Euclidean distance in . Scalar product. Sequences in . Topology and metrics in . Eigenvalues and eigenvectors. Diagonalization of matrices. Properties of eigenvalues.
Part II: Calculus of functions of several variables:
Continuous functions and Weierstrass theorem. Concave or convex functions. Partial derivatives and gradient. Differential. Derivations along a curve and directional derivative. Second order derivatives. Schwarz's theorem. Hessian matrix. Implicit function thoerem. Comparative statics. Inverse function theorem. Quadratic forms and matrices. Sign of a quadratic form.
Part III: Optimization:
Local and global maximum or minimum. First order conditions and second order conditions for free optimization. Equality constraints. Inequality constraints. Substitution method. Lagrange multiplier theorem. Second order conditions with constraints. Optimization for convex functions. Economic applications.
Part IV: Ordinary differential equations and systems
Definitions and examples. Exact differential. Equations in separable variables. Exact equations. Homogeneous equations. Malthusian growth model. Logistic growth model. Second order linear differential equations. General theorem of existence and uniqueness of the solution. Field of directions. Economic applications. Two-dimensional differential equation systems. Systems of linear differential equations: resolving method using eigenvalues, stationary states and their stability. Economic applications.

Simon & Blume: “Matematica per le scienze economiche” ed. Egea.
Other materials will be available in the course Moodle class

Other Textbooks:
Mastroeni L. and Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.

1. The public administration and its law - Legal system and administration: the constitutional discipline. Legal sources of administrative law.
2. Administrative organization: general outlines - The evolution of the State - Liberal state and welfare state - Sizing of the welfare state and European law - The State, the ministries - Other public bodies and local autonomies - Agencies - Independent administrative authorities - The privatization of economic public bodies - Public companies - Public goods and services.
3. The employment relationship with the public administration - Privatization - Government bodies and public management.
4. The subjective juridical situations towards the public administration - The administrative procedure - The administrative acts: validity and efficacy. – Self-defense
5. Transparency and right of access
6. Obligations, contracts and responsibilities of the public administration

ALBERTO ROMANO (a cura di), Diritto amministrativo, Torino, Giappichelli, 2023

The course is structured in three parts:
1) The company and the strategy
2) The functions of company management
3) Operational management

Specifically, the course deals with:
Firms and their roles
Firm and their environment
Stakeholders theory
Theory of the firm
Strategic management of the company
The competitive analysis
Evolution of sectors and competitive structures
The Resource Based View
The competitive advantage
The growth of the company
The roles of corporate management: management, programming, control, human resources, information systems, knowledge management
Operational management: marketing, production, finance, logistics, innovation, administration

Please refer to the official page of the course.

Attending students
• Textbook: Sciarelli, La gestione dell'impresa. Tra teoria e pratica aziendale
• Additional materials shared on the virtual class (MS Teams)
• Notes

Non-Attending students
• Textbook: Sciarelli, La gestione dell'impresa. Tra teoria e pratica aziendale
• Additional materials shared on the virtual class (MS Teams)

Students interested in better examining the topics are kindly invited to discuss them with the instructor.

This course presents the latest thinking in economic development with a comprehensive approach. The pace and scope of economic development continues its rapid, uneven, and sometimes unexpected evolution. This course explains the unprecedented progress that has been made in many parts of the developing world, but fully confronts the enormous problems and challenges that remain to be addressed in the years ahead. The course shows the wide diversity across the developing world in their extent of economic development and other characteristics; and the differing positions in the global economy that are held by developing countries. The field of economic development is versatile and has much to contribute regarding these differing scenarios. Thus, the course also underlines common features that are exhibited by a majority of developing nations, using the insights of the study of economic development. The still relatively small number of countries that have essentially completed the transformation to become developed economies, such as South Korea and Singapore, are also examined as potential examples for other developing countries to follow. Both theory and empirical analysis in development economics have made major strides, and this course brings these ideas and findings to students. Development economics provides critical insights into how we got to where we are, how great progress has been made in recent years, and why many development problems remain so difficult to solve. The principles of development economics are also key to the design of successful economic development policy and programs as we look ahead. At the same time, international development is an interdisciplinary subject, in which approaches and insights from anthropology, finance, geography, health sciences, political science, psychology, and sociology have had significant influence on the subject, and are considered throughout the text. Some approaches that began as explicit critiques and alternatives to what were then limits to development economics have become central to its study. For example, behavioral economics and experimental research now play central roles in the field. Legitimate controversies are actively debated in development economics, and so the text presents contending theories and interpretations of evidence, with three goals. The first goal is to ensure that students understand real conditions and institutions across the developing world. The second is to help students develop analytic skills while broadening their perspectives of the wide scope of the field. The third is to provide students with the resources to draw independent conclusions as they confront development problems, their sometimes ambiguous evidence, and real-life development policy choices—ultimately, to play an informed role in the struggle for economic development and ending extreme poverty.

1 Introducing Economic Development: A Global Perspective. Sustainable Development and Agenda 2030.
2 Comparative Economic Development
3 Classic Theories of Economic Growth and Development
4 Contemporary Models of Development and Underdevelopment
5 Poverty, Inequality, and Development
6 Population Growth and Economic Development: Causes, Consequences, and Controversies
7 Urbanization and Rural-Urban Migration: Theory and Policy
8 Human Capital: Education and Health in Economic Development
9 Agricultural Transformation and Rural Development
10 The Environment and Development
11 Development Policymaking and the Roles of Market, State, and Civil Society
12 International Trade Theory and Development Strategy
13 Balance of Payments, Debt, Financial Crises, and Sustainable Recovery: Cases and Policies
14 Foreign Finance, Investment, Aid, and Conflict: Controversies and Opportunities
15 Finance and Fiscal Policy for Development

Todaro, M.P., and S.C. Smith. Economic Development. 13th edition. Pearson Education, 2020. ISBN:978-1292291154, only chapters 1 to 10, excluding chapters 11 to 15

• Integrated approach between economics and environment
• Sustainable development
• Environmental degradation and market failures
• The Coase's Theorem
• Environmental taxes and environmental standards
• Tradable permits
• Other policy instruments: environmental subsidies and liability
• Cost-benefit analysis
• Economics of climate change
• Economics of natural resources
• Economics of natural disasters
• Circular economy and the just and sustainable transition

Turner KR, Pearce DW, Bateman I (2003) Economia Ambientale, Il Mulino.

Additional teaching material prepared by the lecturer (e.g. slides, lecture notes, publications on scientific journals) will be available on the Moodle platform.

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
First Part: BUSINESS ADMINISTRATION
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identities. Types of firms.
2) The firm in its economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and profitability. Information Systems Governance and Internal controls (overview). Planning in business (overview).
Second Parte: ACCRUAL ACCOUNTING
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

First Part: Business Administration
Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2° edizione, 2021
Onida, P., Economia d'azienda, Utet, Torino, 1970
Zanda, G., Lineamenti di Economia Aziendale, Edizioni Kappa, Roma, 2006

Second Part: Accrual Accounting
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2° edizione, 2020
For business administration and accounting exercises:
Paoloni M. (a cura di), Mattei G., Paoloni, N., Eserciziario di economia aziendale e contabilità, CEDAM, 2018

Syllabus
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Robert N. Anthony – Leslie K. Breitner, Essentials of Accounting, Prentice Hall, 2007
Slides/teaching notes will be available on the website

1. National accounting system: basic defintions and identities. Main macroeconomic indicators
2. Keynes’s theory: aggregate demand and equilibrium output
3. Keynes’s theory: money and interest
4. The IS-LM model
5. The AS-AD model
6. Inflation and unemployment
7. Macroeconomics of the European Union
8. Money: creation and control

Compulsory material:
1) Textbook: Antonella Stirati, Fondamenti di macroeconomia, Giappichelli, ISBN 9791221108514 (forthcoming in September 2024. Check the detailed programme for precise indications on the parts of the textbook to be studied). Students may ask for alternative material in English. Please contact prof Palumbo
2) Additional teaching material (lecture notes, slides, etc, made available on the moodle website)

The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

Fondamenti di Macroeconomia, elementi di base, di Antonella Stirati; Giappichelli 2024

Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.
Limits:
Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Integral calculus:
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

Suggested materials:
- Notes can be downloaded online from the course Matematica Generale on Moodle at the website: https://economia.el.uniroma3.it/
Optional materials:
- Loretta Mastroeni, Alessandro Mazzoccoli, Pierluigi Vellucci. Esercizi di matematica generale. Esculapio, 2023

Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.

Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.

Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.

Real functions of a real variable:

Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.

Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.

Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).

Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).

Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.

Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.

Linear algebra:

Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.

Integral calculus:

Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(w.p.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.

(w.p.) = “with proof”

Suggested materials:

- Mastroeni, Mazzoccoli, Vellucci: "Esercizi di matematica generale". Società editrice Esculapio. ISBN 9788893853910

Optional materials:

-Peccati, Salsa, Squellati. "Matematica per l'economia e l'azienda". Egea.

-Bramanti, Pagani, Salsa. Calcolo infinitesimale e algebra lineare Seconda edizione

- Alberto Bersani, Francesco Manzini, Loretta Mastroeni. Esercizi di Matematica Generale: Per i corsi del nuovo ordinamento delle Facoltà di Economia. Società Editrice Esculapio, 2009.

Introduction to computer science
Computer architecture
CPU, main memory, secondary memory, input/output peripherals
The operating system and application software
Overview of text document editors
Creating and managing text documents
Tools for formatting text, images, tables, and styles in text documents
Review capabilities of a text document
Advanced features for text documents
Spreadsheet overview
Cells, formulas and major spreadsheet features
Using functions and constructing charts in spreadsheets
Advanced features for spreadsheets

Materials provided by the lecturer

The program includes:
Introduction to law
Forms of State and forms of Government
Beyond the State: the EU
The sources of law
Parliament and its functions
Institutes of direct democracy
The abrogative referendum.
The Government and its functions
The President of the Republic and his attributions
Principles on the subject of Administration
The other organs
Local ordering
Rights and freedom
The economic Constitution
Judicial power
Constitutional Justice

It is recommended the study of one of the following books:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, latest edition
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, latest edition
F. Modugno (a cura di), Diritto Pubblico, Torino, Giappichelli, latest edition
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, latest edition

The Public Law course is divided into two modules.
Module I covers the following topics: theory of social groups; the normative social groups; the structure of the legal system; power and its species; power-sharing techniques; the forms of exercise of power: the legal norm and the provision; subjects; interests; the goods; subjective legal situations; the legal facts; human behaviors; the legal effects; the responsability; the regulatory levels of government (international, European Community, state, local); the organization of public authorities; public functions (political direction, regulation, administration, jurisdiction).
The II Module deals with the Italian legal system and the regulatory principles of its political, legislative, administrative and jurisdictional activity.

For preparation for Modules I and II we recommend studying a manual chosen from the following:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, ult. ed.
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, ult. ed.
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, ult. ed.

Detailed program by chapters.
Part 1. Introduction
Chapter 1. Thinking as an economist (all)
Chapter 2. Supply and Demand (All)
Part 2. Consumer theory.
Chapter 3. Rational consumer choice (all but par. 3.5)
Chapter 4. The utility function (all except par. 4.6.4)
Chapter 5. The applications of rational choice and demand: paragraphs 5.4 and 5.4.1 only.
Part 3. Business theory and market structure.
Chapter 9. Production (all). Appendix to Chapter 9: A.9.1, A.9.2, A.9.2 only
Chapter 10. Costs (all except Section 10.7)
Chapter 11. Perfect competition (all except 11.11.1, 11.12.1, 11.12.2, 11.12.3, 11.14)
Chapter 12. Monopoly (all but paragraph 12.9)

R.H. Frank e E. Cartwright (2021) Microeconomia, VIII edizione. Milano: McGraw-Hill

Elements of the theory of production
- inputs, outputs and production methods
- the subsistence economy
- the economy with a surplus
The surplus approach to commodity value and income distribution
- the relevance of social and institutional elements to income distribution
- the explanation of the real wage rate
- the "core" of the classical approach
- the link between profit rate and relative prices
- the price equations
- the classical theory of rent
The theory of consumer choice
- budget set and budget constraint
- preferences
- consumer choice
- consumer-good demand curves
The theory of firm choice
- the function of production
- profit maximisation
- isoquants and isocosts
- the output expansion path and long-term cost curves
Production factors and the marginalist explanation of income distribution
- marginal and average productivity of factors
- the demand curves of factors of production
- equilibrium between supply and demand for factors of production
Market forms
- perfect competition
- monopoly
- Cournot oligopoly
- Stackelberg oligopoly
Introduction to the welfare economics
- allocations and Edgeworth box
- Pareto improvements and Pareto optima
- first theorem of welfare economics

i) “Elementi di teoria della produzione”, Dispensa n. 1 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
ii) “La teoria classica della distribuzione e dei prezzi relativi”, Dispensa n. 2 (materiale didattico redatto da R. Ciccone, S.M. Fratini e A. Trezzini).
iii) “Teoria marginalista della distribuzione”, Dispensa n. 3 (materiale didattico redatto da S.M. Fratini).
iv) Frank Robert H.; Cartwright Edward; Piras R. Microeconomia. McGraw-Hill Libri Italia, Milano. 2021.
v) “Glossario ed Esercizi Svolti di Microeconomia” (materiale didattico redatto da S.M. Fratini e D. Pignalosa).

An introduction to the fundamental ideas of statistics. Topics include:

Descriptive statistics: graphical summaries of data, measuring the center of quantitative data (mode, median, mean), measuring the variability of quantitative data (standard deviation, variance), simmetry of a distribution (Fisher coefficient), the association between two variables (chi-square), the association between two quantitative variables (covariance, correlation coefficient).

Probability: probability of events (probability of the complement of an event, of the union and intersection of two events, conditional probability, independent events, Bayes theorem), discrete and continuous random variables (the Bernoully r.v., the Binomial r.v., the Poisson r.v., the Normal r.v., the Student t r.v., che Chi-square r.v.).

Inferential statistics: sample versus population, sampling distributions, point and interval estimates of population parameters, confidence intervals for a population mean and a proportion, significance tests about hypotheses on a population mean and a proportion, p-values.

Regression analysis: the regression line, ordinary least squares, describing the strength of the association, nonlinear regression models, confidence intervals and tests on the parameters of the regression line, prediction.

G.Cicchitelli, P.D'Urso, M.Minozzo. Statistica: principi e metodi. Pearson, fourth edition:
Chap. 1 (excluding 1.11), Chap. 2 (excluding 2.4, 2.5), Chap. 3 (excluding 3.4, 3.5, 3.6), Chap. 4 (excluding 4.3, 4.4, 4.5, 4.6, 4.15), Chap. 5 (excluding 5.3, 5.6, 5.7, 5.8), Chap. 6 (excluding 6.3), Chap. 9 (excluding 9.3), Chap. 10, Chap. 11 (excluding 11.2.1), Chap. 12, Chap. 13, Chap. 14 (excluding 14.2, 14.6, 14.7),Chap. 17 (excluding 17.6), Chap.18 (excluding 18.3, 18.4), Chap. 19 (excluding 19.5), Chap. 20 (excluding 20.6, 20.7), Chap. 22 (excluding 22.2.2), Chap. 23.

A collection of exercises by the teacher is available to students on Moodle.

Descriptive statistics:
variables and their measurement, univariate distributions, describing data with tables and graphs, measures of position, variability.
Bivariate descriptive statistics: independence, association, correlation, probability distributions for discrete and continuous variables, sampling distributions
Inference: estimation, hypothesis test, regression

A. Agresti, B. Finlay. Statistical methods for the social sciences. Pearson International Edition-4th edition (2009)

Part 1 - The theory of Financial Statements
-Introduction to the study of the Financial Statements
- The basic functions of the Financial Statements
- The nature of income and capital
- The purposes of the Financial Statements
- The relationship between income, evaluation criteria and purposes of the Financial Statements
- The goals of the Financial Statements in corporate doctrine: the "alpha" goal and the "beta" goal

Part 2 - The Financial Statements according to the Civil Code
- The Financial Statement documents - Structure and content (Articles 2423-ter - 2425 of the Italian Civil Code)
- The general clause and the principles for preparing the Financial Statements (articles 2423 - 2423-bis of the Italian Civil Code)
- The specific evaluation criteria (art. 2426 of the civil code)
- Fixed assets
- Receivables
- Inventories (Lifo, Fifo, Cmp)
- Work in progress assets
- The content of the Notes and the Management Report

Part 3 – Accounting
- Closing accounting entries, general closure and reopening of accounts
- Fixed assets – Depreciation, amortization and devaluation
- Financial Investments – Equity Method
- Inventories and work in progress – FIFO, LIFO and WACC

Part 4 - Fundamentals of financial statement analysis
- Reclassification of BS and IS
- Ratios
- Statement of Cash Flows – Direct and Indirect Method

Suggested readings:

Part 1 and 2: Tutino M. (2017), Bilancio e nuovi OIC, Cedam
Part 3: Paoloni M., Celli M. (2012), Introduzione alla contabilità generale, Cedam
Part 4: Paolucci G. (2016), Analisi di Bilancio, Hoepli

Slides and exercises available on the Professor's web page

The course addresses the following topics:

1. Theoretical models of public intervention: welfare economics; the new welfare economics; market failures;
2. The critical aspects of the new welfare economics;
3. Alternative approaches to welfare economics for collective decisions: the Musgrave model; the Lindahl model; the Johansen model; the Buchanan model;
4. The formation of collective decisions;
5. The theory of taxation;
6. Shifting and incidence of taxes;
7. The effects of taxes on choices between consumer goods, between work and leisure, between consumption and savings;
8. The excess burden of taxes;
9. Overview of the theory of optimal taxation.

1. for the general part, a text will be made available to students at the beginning of the course in pdf format;

2) for the section on the Italian tax system: Bosi P., Guerra M.C., I tributi nell'economia italiana, Il Mulino, Bologna, ed. 2023, capitoli III, IV, V, VI, VII, VIII

Main official statistical surveys: data production and interpretation. In particular: Consumer prices, Industrial production, Labour forces, Household consumptions, Income and living conditions, Household Income and Wealth. National accounts. Main statistical indicators for economic phenomena: (simple and complex) index numbers, measures of concentration.
Calendar adjusted and seasonal adjusted time series; chain-linked values. The use of moving averages to reconstruct the trend.
Introduction to econometrics. Single and multiple Linear Regression: ordinary least squares, goodness of fit, homoscedasticity and heteroscedasticity. Nonlinear regression functions. Regression with panel data. Regression with a binary dependent variable.
An introduction to the use of R for statistical analysis.

Class notes (in Italian) downloadable from the Moodle space of the course.
Press releases (Istat - Banca d'Italia).
Stock J.H. and Watson M.W., Introduction to Econometrics, Global edition, 4th Edition, 2020, Pearson.

PARTE GENERALE
- Nozioni introduttive: la norma e l’ordinamento giuridico. Le fonti del diritto e i conflitti tra le stesse. Il diritto privato. L’interpretazione della legge e l’analogia.
- Le situazioni giuridiche soggettive e i rapporti giuridici.
- Il soggetto del rapporto giuridico: persone fisiche e persone giuridiche. I diritti della personalità.
- L’oggetto del rapporto giuridico: i beni. I diritti reali: proprietà, possesso, diritti reali di godimento. Comunione e condominio. L’usucapione.
- Il rapporto obbligatorio: adempimento, inadempimento, vicende dell’obbligazione, tipologie di obbligazioni, tutela del credito e garanzie dell’obbligazione.
- Atto, fatto e negozio giuridico. Il contratto: il contratto in generale, formazione e vicende del contratto, le patologie, i singoli contratti nominati.
- I fatti illeciti e le altre fonti delle obbligazioni.
- La tutela dei diritti: la trascrizione. I diritti reali di garanzia, le azioni a difesa della garanzia patrimoniale, la prescrizione e la decadenza.
PARTE SPECIALE
- Diritti e tutele delle persone minori di età

FUNDAMENTAL/GENERAL PART
One of the following Manuals, alternative to each other, as long as they are updated to the latest edition:
- S. MAZZAMUTO (a cura di), Manuale di diritto privato, Giappichelli, Torino, ult. ed, (Parte I, II (excluded cap. V), parte V, VI, VII, VIII)
- L. NIVARRA, V. RICCIUTO, C. SCOGNAMIGLIO, Istituzioni di diritto privato, Torino, ult. ed. (excluded cap. XIII e XIV)
- P. PERLINGIERI, Istituzioni di diritto civile, Edizioni Scientifiche Italiane, Napoli, ult. ed. (excluded parte VI, VII e VIII)
- A. TORRENTE e P. SCHLESINGER, Manuale di diritto privato, Giuffré, Milano, ult. ed. (until cap. LV; excluded cap. LII e LIII)

SPECIAL PART
ETTORE BATTELLI, Diritto privato delle persone minori di età, Giappichelli, Torino, 2021 (p.1-155).

To follow the lessons, it is essential:
A. DI MAJO (eds), Codice Civile, Giuffrè, Milano, last edition.
G. PERLINGIERI e M. ANGELONE (a cura di), Codice civile, ESI, Napoli, last edition

Part I: Linear algebra
The real n-dimensional vector space. Linear dependence and independence. Subspaces and spaces generated by vectors. Bases. Algebra of matrices. Determinant. Inverse matrix. Rank of a matrix. Systems of linear equations. Cramer's Theorem and Rouché-Capelli's Theorem. Homogeneous systems and linear dependence. Norm and Euclidean distance in . Scalar product. Sequences in . Topology and metrics in . Eigenvalues and eigenvectors. Diagonalization of matrices. Properties of eigenvalues.
Part II: Calculus of functions of several variables:
Continuous functions and Weierstrass theorem. Concave or convex functions. Partial derivatives and gradient. Differential. Derivations along a curve and directional derivative. Second order derivatives. Schwarz's theorem. Hessian matrix. Implicit function thoerem. Comparative statics. Inverse function theorem. Quadratic forms and matrices. Sign of a quadratic form.
Part III: Optimization:
Local and global maximum or minimum. First order conditions and second order conditions for free optimization. Equality constraints. Inequality constraints. Substitution method. Lagrange multiplier theorem. Second order conditions with constraints. Optimization for convex functions. Economic applications.
Part IV: Ordinary differential equations and systems
Definitions and examples. Exact differential. Equations in separable variables. Exact equations. Homogeneous equations. Malthusian growth model. Logistic growth model. Second order linear differential equations. General theorem of existence and uniqueness of the solution. Field of directions. Economic applications. Two-dimensional differential equation systems. Systems of linear differential equations: resolving method using eigenvalues, stationary states and their stability. Economic applications.

Simon & Blume: “Matematica per le scienze economiche” ed. Egea.
Other materials will be available in the course Moodle class

Other Textbooks:
Mastroeni L. and Mazzoccoli A.: “Matematica per le applicazioni economiche” ed. Pearson.

1. Concepts, Issues
2. Welfare economics
3. Redistributive policies
4. Imperfect competition, externalities, industrial policy, regional policies
5. Labour market policies
6. Fiscal Policy
7. Monetary Policy
8. Financial Stability
9. Macroeconomic policies in an open economy
10. Growth Policies

R Cellini, Politica Economica, McGraw Hill, 2019

1. The public administration and its law - Legal system and administration: the constitutional discipline. Legal sources of administrative law.
2. Administrative organization: general outlines - The evolution of the State - Liberal state and welfare state - Sizing of the welfare state and European law - The State, the ministries - Other public bodies and local autonomies - Agencies - Independent administrative authorities - The privatization of economic public bodies - Public companies - Public goods and services.
3. The employment relationship with the public administration - Privatization - Government bodies and public management.
4. The subjective juridical situations towards the public administration - The administrative procedure - The administrative acts: validity and efficacy. – Self-defense
5. Transparency and right of access
6. Obligations, contracts and responsibilities of the public administration

ALBERTO ROMANO (a cura di), Diritto amministrativo, Torino, Giappichelli, 2023

MODULE 2:
IV. THE DETERMINATION OF OUTPUT IN THE TWO THEORETICAL APPROACHES
V. KEYNES’S GENERAL THEORY.
VI. THE NEOCLASSICAL SYNTHESIS AND THE IMPAIRMENT OF THE KEYNESIAN REVOLUTION

All didactic material will be either given or indicated to students at the beginning of the course and made available on the moodle website.

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
First Part: BUSINESS ADMINISTRATION
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identities. Types of firms.
2) The firm in its economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and profitability. Information Systems Governance and Internal controls (overview). Planning in business (overview).
Second Parte: ACCRUAL ACCOUNTING
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

First Part: Business Administration
Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2° edizione, 2021
Onida, P., Economia d'azienda, Utet, Torino, 1970
Zanda, G., Lineamenti di Economia Aziendale, Edizioni Kappa, Roma, 2006

Second Part: Accrual Accounting
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2° edizione, 2020
For business administration and accounting exercises:
Paoloni M. (a cura di), Mattei G., Paoloni, N., Eserciziario di economia aziendale e contabilità, CEDAM, 2018

Syllabus
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Robert N. Anthony – Leslie K. Breitner, Essentials of Accounting, Prentice Hall, 2007
Slides/teaching notes will be available on the website

1. National accounting system: basic defintions and identities. Main macroeconomic indicators
2. Keynes’s theory: aggregate demand and equilibrium output
3. Keynes’s theory: money and interest
4. The IS-LM model
5. The AS-AD model
6. Inflation and unemployment
7. Macroeconomics of the European Union
8. Money: creation and control

Compulsory material:
1) Textbook: Antonella Stirati, Fondamenti di macroeconomia, Giappichelli, ISBN 9791221108514 (forthcoming in September 2024. Check the detailed programme for precise indications on the parts of the textbook to be studied). Students may ask for alternative material in English. Please contact prof Palumbo
2) Additional teaching material (lecture notes, slides, etc, made available on the moodle website)

The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

Fondamenti di Macroeconomia, elementi di base, di Antonella Stirati; Giappichelli 2024

Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.
Limits:
Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Integral calculus:
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

Suggested materials:
- Notes can be downloaded online from the course Matematica Generale on Moodle at the website: https://economia.el.uniroma3.it/
Optional materials:
- Loretta Mastroeni, Alessandro Mazzoccoli, Pierluigi Vellucci. Esercizi di matematica generale. Esculapio, 2023

Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.

Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.

Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.

Real functions of a real variable:

Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Composition function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function. Definition of a sequence.

Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.

Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).

Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).

Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem’s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.

Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.

Linear algebra:

Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.

Integral calculus:

Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(w.p.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.

(w.p.) = “with proof”

Suggested materials:

- Mastroeni, Mazzoccoli, Vellucci: "Esercizi di matematica generale". Società editrice Esculapio. ISBN 9788893853910

Optional materials:

-Peccati, Salsa, Squellati. "Matematica per l'economia e l'azienda". Egea.

-Bramanti, Pagani, Salsa. Calcolo infinitesimale e algebra lineare Seconda edizione

- Alberto Bersani, Francesco Manzini, Loretta Mastroeni. Esercizi di Matematica Generale: Per i corsi del nuovo ordinamento delle Facoltà di Economia. Società Editrice Esculapio, 2009.