MATEMATICA GENERALE
MATHEMATICS
9 ECTS
Lecturer:
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Elena Molho A-K
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molhoe@eco.unipv.it
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Giorgio Giorgi L-Z
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ggiorgi@eco.unipv.it
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Assistants:
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Elisa Caprari
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elisa.caprari@unipv.it
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Mario Maggi
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maggma@unipv.it
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Course Program
Linear algebra. Vectors in Rn. Linear space. Linear dependence. Basis and dimension of a linear space. Matices. Daterminant. Inverse matrix. Rank. Systems of linear equations.
Topology on R. Limits: definition, theorems, operations, calculus. Continuous functions and their properties.
Differential calculus of functions of one real variable. The derivative and its geometric
interpretation. Higher order derivatives. Continuity and derivability. Differentiation rules.
Stationary points. Some fundamental theorems in differentiable analysis: Rolle, Lagrange,
Hospital. Maxima and minima of derivable functions. The differential. Taylor formula.
Concavity and convexity. Asymptotes. Study of the diagram of a function.
Integral calculus of functions of one real variable. The indefinite integral and integration methods (decomposition, by parts, by substitution). The definite integral and its geometric interpretation. The mean value theorem. The fundamental theorem for integral calculus. Generalized integrals.
Functions of more than one variables. Introductory notions. Partial derivatives and gradient vector. Differentiability. Second order partial derivatives and hessian matrix. Maxima and minima.
Educational Aim
The course offers an introduction to some basic instruments in Calculus and Linear Algebra that are used in a quantitative approach to economic and business models.
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Reading List
Chiang, A.C., Fundamental Methods of Mathematical Economics, Mc Graw-Hill, Singapore, 1984
Simon, C.P. And Blume, L.E., Mathematics for Economists, W.W.Norton &Company.
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Assessment
Written exam with the possibility of an oral exam if the marks in the written exam is at least 24/30.
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MATEMATICA PER L’ECONOMIA E LA FINANZA
MATHEMATICS FOR ECONOMICS AND FINANCE
9 ECTS
Undergraduate
Lecturer:
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Giorgio Giorgi
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ggiorgi@eco.unipv.it
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Assistant:
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Elisa Caprari
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elisa.caprari@unipv.it
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Course Program
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ELEMENTS OF LINEAR ALGEBRA.
Structure of a linear (or vector) space. Basic notions on vectoris in Rn. Notion of linear dependence and independence of vectors in Rn, of dimension and of base for a linear subspace of Rn. Linear mappings and representation theorem. Eigenvalues and eigenvectors; eigenspace; algebraic muliplicity of eigenvalues and geometric multiplicity; necessary and sufficient conditions to have n eigenvectors linearly independent; sufficient conditions to get the same property. Eigenvalues and eigenvectors of symmetric matrices. Similarity transformations and diagonalization of square matrices. Schur theorem. Jordan canonical form. Cayley-Hamilton theorem. Quadratic forms: classification and criteria to ascertain their sign (by means of eigenvalues and by means of principal minors). Constrained quadratic forms. Spectral radius. Matrix power series (“series of C. Neumann”). Nonnegative square matrices and Perron-Frobenius theorems. The Leontief economic model. The Sraffa model.
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FUNCTIONS OF SEVERAL VARIABLES.
Basic notions on differential calculus for functions of several variables; partial derivatives (of first order and of second order). Jacobian matrix and Hessian matrix. Differentiable functions. Equation of the tangent hyperplane to a surface. Chain rule for a composed function. Directional derivatives. Homogeneous functions: definition, main properties, Euler theorem. Implicit functions and related theorems. Taylor formula for functions of several variables.
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OPTIMIZATION.
Unconstrained optimization problems and constrained optimization problems. Weierstrass theorem. Unconstrained optima and Fermat theorem. Sufficient second-order optimality conditions for unconstrained optimization problems. Optimization problems with an abstract constraint (set constraint). Convex and concave functions; strictly convex (strictly concave) functions. Characterization of differentiable convex (concave) functions; characterization of twice-continuously differentiable convex (concave) functions. Application of convex (concave) functions to unconstrained optimizationn problems. Linear combination and composition of convex functions. Quasiconvex and pseudoconvex functions; their characterizations for differentiable functions and for twice-continuously differentiable functions. Constrained optimization problems with equality constraints. The case of two variables (and one constraint): method of transforming a constrained problem into an unconstrained one, geometric method, Lagrange multipliers method. The general case (n variables): necessary optimality conditions and sufficient (second-order) optimality conditions. Economic interpretation of the Lagrange multipliers (sensitivity analysis and “shadow prices”). Constrained optimization problems with equality constraints (mathematical programming problems). Gordan theorem of the alternative. Abadie and F. John necessary optimality conditions. Constraint qualifications: Arrow-Hurwicz-Uzawa condition and its generalization, linear independence condition, Slater condition. Kuhn-Tucker necessary optimality conditions. Kuhn-Tucker sufficient optimality conditions. Mathematical programming problems with nonnegative variables. Method of the contour lines and of “restrictions” for the bidimensional case. The convex (concave) programming problem; saddle points of the Lagrangian function. Fan-Gliscksberg-Hoffman theorem of the alternative. Relationships between saddle points of the Lagrangian function and the Kuhn-Tucker conditions. Linear programming (L. P.): basic notions and classifications. Convex polyhedrons. Findamental theorem on L. P.. geometric solution for the bidimensional case. Basic solutions, feasible basic solutions and related theorem. Dual problems: basic definitions and notions. Existence theorem, weak duality theorem, duality theorem, complementary slackness theorem.
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DYNAMIC SYSTEMS.
Continuous and discrete dynamic systems. Differential equations: basic notions. Systems of first order differential equations. Existence of solutions. Uniqueness of a solution. First order linear differential equations. Systems of first order linear differential equations. Systems of first order linear differential equations with constant coefficients. Equilibrium solutions. Stability notions. Application to the case of a system of linear differential equations with constant coefficients: Routh-Hurwicz conditions, dominant and quasi-dominant diagonal matrices. Geometric methods for the stability of unidimensional systems (“phase diagrams”). Analytical methods for multidimensional systems: the Lyapunov “second method” and the linearization method. Application to the study of the stability of the equilibrium for a Walrasian economic system.
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OUTLINES ON DISCRETE DYNAMIC SYSTEMS.
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OUTLINES ON DOUBLES INTEGRALS
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Educational Aim
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The aim of the present course is to deepen some aspects of the program of the course “general mathematics” (first year) and, above all, to provide the students with those mathematical tools and subjects, used in economic theory and related areas.
all subjects concerning linear algebra and funcions of several variables, learned in the course of “general mathematics”, are to be known by the students attending the present course.
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Reading List
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Simon, C.P. and Blume, L. E., Mathematics for Economists, W. W. Norton & Co., New York.
Chiang, A. C., Fundamental Methods of Mathematical Economics, Mc Graw-Hill, New York.
Mangasarian, O. L., Nonlinear Programming, Mc Graw-Hill, New York.
Takayama A., Mathematical Economics, Cambridge Univ. Press, Cambridge.
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Assessment
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Written and oral exam.
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MERCATI INTERNAZIONALI DEI PRODOTTI AGRICOLI
INTERNATIONAL TRADE OF AGRICULTURAL PRODUCTS
6 ECTS
Lecturer:
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Carlo Bernini Carri
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cbernini@eco.unipv.it
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Course Program
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International trade theories and commodities.
Trends in the global and agricultural trade;
The role of commodities in the international trade;
Agricultural commodity markets: past development and outlook;
Multinational firms and primary commodity
The main theories of the international trade.
Basic concepts: economic benefits of trade and the comparative advantage theory according to the classical and neo-classical approach.
The new theoretical formulations: the technological gap theory; the life cicle theory; the representative demand theory; etc.
Protectionism vs free trade
Economic and non-economic factors for protectionism; food security and protectionism.
Policies for trade at a national (tariffs, quotas, etc.) and international (price stabilisation schemes, etc.) level.
Economic effects of trade policies: tradable and non tradable goods; partial equilibriummodel for the analysis of a single industry.
Measurement of the protectionism level: nominal and effective protectionism coefficients; producer and consumer support estimate; aggregate measurement of support.
Statistical indicators to evaluate the specialization degree of a country and the performances of its trading sectors.
International agreements and agriculture
Regional integration processes: main types in the trade unions; trade creation and trade diversion effects.
Gatt and WTO: concepts and rules; Gatt and trade liberalization. Urugay round and Agreement on Agriculture (AoA).
From Gatt to WTO: a new round.
A predictable agreement and its effects; the different interests among the group of countries.
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Educational Aim
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The course provides the economic analysis of the agribusiness management through the understanding of the relationships across the production units of the system and the state and functioning of the agribusiness market. A specific attention is dedicated to the tools for the management decision making process.
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Reading List
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Specific issues are available.
Other lectures:
Dominick S., Economia Internazionale, NIS, 1999.
Berrnini Carri C., Trade liberalization, growth and food security, Aracne Ed., 2009.
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MICROECONOMIA
MICROECONOMICS
9 ECTS
Lecturer:
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Giorgio Rampa A-K
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giorgio.rampa@unipv.it
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Lorenzo Rampa L-Z
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rampa@eco.unipv.it
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Course Program
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Principle of choice theory; equilibrium notion
Consumption, demand, consumer surplus
Information, choice under uncertainty, insurances
Production, costs, profits, supply
Competitive equilibrium and efficiency
Monopoly and efficiency
Games and oligopoly
Externalities and public goods
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Educational Aim
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The course offers the fundamentals of the theory of individual choice (consumption, production, under uncertainty and under strategic interaction), of market equilibria, and of their efficiency properties. The themes of perfect and imperfect competition, and of externalities, are dealt with.
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Reading List
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R.H. Frank, Microeconomia, McGraw-Hill, Milano, 2010
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Assessment
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Written exam, plus possible oral exam
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ORGANIZZAZIONE AZIENDALE
ORGANIZATIONAL THEORY AND DESIGN
6 AND 9 ECTS
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Lecturer:
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Alberto Francesconi
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alberto.francesconi@unipv.it
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Assistants:
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Claudia Dossena
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claudia.dossena@eco.unipv.it
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6 ECTS
Course Program
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The course concerns the principles of management in terms of organizational design. Both levels of the firm (as a whole) and single organizational units are analyzed. The attention is focused on the reciprocal relations between strategy, technology, environment and organizational variables. The main topics proposed are:
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organizational analysis and design, both from recent and consolidated perspective;
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reciprocal link between strategic and organizational choices, such as resources-based view and dynamic capabilities paradigms
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organizational forms: basic and complex structures
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job design (basic issues)
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environmental pressure on organizational design;
The course balances theory and empirical issues also through the discussion of case studies. Main features and evolution of contemporary economy are considered.
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Educational Aim
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The course aims at supplying basic knowledge in terms of organizational design in both profit and non profit organizations under the constraints of efficiency and effectiveness. Students will become comfortable with main organizational issues and models to interpret the human behaviours and to design structures and operating mechanisms at firm level and within single organizational units
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Reading List
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Francesconi A., Dispensa di organizzazione aziendale, testo e casi. A.A. 2010-2011 (teaching materials, text and cases);
Rugiadini A. (1979), Organizzazione di impresa, Giuffrè, Milano
Other suggested
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Tosi H.L., Pilati M., 2008, Comportamento organizzativo. Attori, relazioni, organizzazione, management, Milano, Egea;
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Morgan G., 2002, Images. Le metafore dell’organizzazione, 2° ed., Franco Angeli, Milano;
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Costa G. e Nacamulli R.C.D., Manuale di organizzazione, Vol. II "La progettazione organizzativa (1997), Vol. III "I processi i sistemi e le funzioni aziendali" (1997), Vol. V "Metodi e tecniche di analisi e intervento" (1996), Torino, Utet Libreria.
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9 ECTS
Course Program
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The course concerns the principles of management in terms of organizational design. Both levels of the firm (as a whole) and single organizational units are analyzed. The attention is focused on the reciprocal relations between strategy, technology, environment and organizational variables. The main topics proposed are:
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organizational analysis and design, both from recent and consolidated perspective;
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reciprocal link between strategic and organizational choices, such as resources-based view and dynamic capabilities paradigms
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organizational forms: basic and complex structures
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job design (basic issues)
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environmental pressure on organizational design;
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business inter-firm networks and organizational solutions for innovation;
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organizational design based on technological features within manufacture and service firms.
The course balances theory and empirical issues also through the discussion of case studies. Main features and evolution of contemporary economy are considered.
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Educational Aim
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The course aims at supplying basic knowledge in terms of organizational design in both profit and non profit organizations under the constraints of efficiency and effectiveness. Students will become comfortable with main organizational issues and models to interpret the human behaviours and to design structures and operating mechanisms at firm level and within single organizational units.
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Reading List
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Daft R.L., 2010, Organizzazione aziendale, Apogeo (Daft R.L., Organization Theory and Design, 10th ed.) selected chapters;
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Francesconi A., Dispensa di organizzazione aziendale, testo e casi. A.A. 2010-2011 (teaching materials, text and cases);
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Rugiadini A. (1979), Organizzazione di impresa, Giuffrè, Milano.
Letture consigliate:
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Tosi H.L., Pilati M., 2008, Comportamento organizzativo. Attori, relazioni, organizzazione, management, Milano, Egea;
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Morgan G., 2002, Images. Le metafore dell’organizzazione, 2° ed., Franco Angeli, Milano;
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Costa G. e Nacamulli R.C.D., Manuale di organizzazione, Vol. II "La progettazione organizzativa (1997), Vol. III "I processi i sistemi e le funzioni aziendali" (1997), Vol. V "Metodi e tecniche di analisi e intervento" (1996), Torino, Utet Libreria.
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Assessment
Written
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