Mathematics for economic applications

Lecturer: Prof. Marco Lonzi

The course covers the following topics. Complex numbers. Linear algebra: Vectorial spaces, Linear applications and linear systems. Eigenvalues and eigenvectors. Simmetric matrices. Diagonalizable matrices. Functions of vectorial variables: differential calculus. Implicit functions. Maximization without and with constrains. Kuhn-Tucker's conditions.

Econometrics I & II

Lecturer: Prof. Federico Crudu

The course provides and introduction to standard regression procedures of parameter estimation and hypothesis testing in economics. The following topics will be covered: simple and multiple regression; least-square estimation; goodness-of-fit; Gauss-Markov theorem; coefficient tests and confidence intervals; multicollinearity; dummy variables; tests on structural change; model misspecification; test of linear restrictions; heteroscedasticity (test and estimation); stochastic regressors; instrumental variables; dynamic models; forecasting; stability test; autocorrelation (test and estimation); introduction to simultaneous equations.

Microeconomics I

Lecturer: Prof. Silvia Tiezzi

The course covers at an advanced level the following topics: preferences and choice; demand and expenditure function; indirect utility and duality; factor demand and cost function; choice under uncertainty; game theory and applications; social choice and mechanism design.

Microeconomics II

Lecturer: Prof. Fabio Petri

The course covers theories of pricing and income distribution with connections with macroeconomics. Detailed list of topics: prices of production; Perron-Frobenius theorem; differential rent; neoclassical approach and general equilibrium; fixed-point theorems; aggregation; problems with capital; degree of utilization; investment theory; first and second theorem of welfare economics; externalities, public goods, Coase theorem; classical approach to wages, efficiency wages, Kalecki on wages and full employment.


Lecturer: Prof. Nicola Dimitri

The course provides the main tools for modern macroeconomic modeling. It covers topics such as consumption, optimal growth and search in the labour market by using the main techniques of dynamic optimization. Further, the course analyzes in detail themes such as monopolistic competition in macroeconomics and coordination failure.

Public Economics

Lecturer: Prof. Massimo D'Antoni

The course is aimed at providing — at an intermediate/advanced level — the conceptual tools necessary to analyse the economic role of the state. The approach emphasizes the relation between theoretical thinking and concrete public policy options. The course focuses on the following topics: private vs public provision of public goods; government expenditure in pensions, health and social protection, with an emphasis on the insurance role of the state; taxation of income, wealth and consumption in theory and in comparative perspective; optimal taxation and the relation between redistribution and efficiency in the design of policies.




Post-Keynesian Economics


Lecturer: Prof. Fabio Petri, Prof. Sergio Cesaratto

The objective of the course is to provide a critical assessment of the different approaches (in their most rigorous formulations) to the theories of value, distribution, employment and growth, overcoming the separation between microeconomics and macroeconomics. Particular attention is paid to the differences between classical, neoclassical, postKeynesian and evolutionary approaches.


Economic Dynamics

Lecturer: Prof. Serena Sordi

The course introduces students to the dynamic analysis of economic phenomena by means of appropriate mathematical methods and with the use of MATLAB for the numerical simulation of the models. By the end of the course students should: (1) be able to study in details the dynamics generated by deterministic models of the economy formulated in terms of both linear differential equations and linear difference equations; (2) be able to perform a full qualitative analysis of nonlinear economic models; (3) have the ability to apply to the study of economic models more advanced tools such as bifurcation theory and chaos theory; (4) have a basic knowledge and understanding of the methods for the simulation of economic dynamic models using MATLAB.


Economic History (not offered in 2017-18)

Lecturer: Prof. Michelangelo Vasta

This advanced course examines the history of world economy over the past two and half centuries. Starting from the British Industrial Revolution and up to the recent time, the course will focus on the main events which characterized the world economy and surveys the onset of modern economic growth. The approach taken is by topics, focussing on the causes of economic development, and the interactions between technology, institutions, political structure and the economy. The goal of the course is to increase the knowledge of world economic history and to improve the ability to think critically, by using different economic theories, about the "lessons" which history can provide.


Finance (Financial Investments and Risk Management)

Lecturer: Prof. Giampaolo Gabbi

The aim of this class is to develop both an ability to make portfolio selection and an appreciation of the wider role of risk management in finance. Candidates will develop an understanding of the decision making process governing the selection of risky assets by investors. On completing this course applicants will be able to: describe advanced methods of calculating the efficient frontier; explain the role of the index and multivariate models in simplifying portfolio selection; calculate the efficient frontier for a portfolio of securities and derivatives.


Growth and Development

Lecturer: Prof. Mauro Caminati

The course aims at providing intermediate level knowledge of land-mark models of economic growth, with a special emphasis on structural change and on convergence and divergence in economic development. The programme includes: the neoclassical growth model and stylized facts about convergence; demand-led growth; exogenous, endogenous and semi-endogenous growth; human capital; models of Schumpeterian growth; competition and innovation; directed technological change; diffusion of technology; trade and Growth; structural change and transformations; market failures and poverty traps; inequality and growth; demographic transition. Topics will be discussed integrating theory with the analysis of historical case studies of growth trajectories.


Industrial Organization

Lecturer: Prof. Luigi Luini

The aim of the course is to help students to become familiar with contemporary topics in advanced industrial organization, both theoretical and applied. The course considers standard topics such as oligopoply, product differentiation, asymmetric information and advertising; it goes on with the economics of networks and standards and intermediated markets; it finally considers applications to the ICT and media industries.


Economic organization and theories of the firm

Lecturers: Prof. Ugo Pagano

The course deals with the different forms of organizations that characterize modern economies. It provides a critical evaluation of the Coasian and New Institutional tradition analyzing markets and firms as costly institutional substitutes. In doing so it considers: the role of public and private orderings in the organization of the economy; the theories and the implications of market incompleteness and of institutional complementarities; the role of the corporations in modern capitalism; intangible assets and intellectual property as engines and constraints of economic development. The second part of the course will focus on the relationship between firm-internal characteristics and knowledge production/innovation, providing some background on additional theories of the firm with respect to those presented in the first part. It uses such theories to consider knowledge production within three forms of firm organization: (a) corporations; (b) small firms/start-ups and (c) peer production.

Monetary Economics

Lecturer: Prof. Alberto Dalmazzo

The course focuses on the working of monetary economies and monetary policies. It starts with the traditional approaches (expected and unexpected shocks, the role of price stickiness and monopolistic competition, time-inconsistency and inflation); it goes on with DSGE models ("classical" and New Keynesian models and monetary policy design); it eventually considers models with credit frictions, which are able to shed some light on the mechanisms of current crisis.