MATHEMATICAL METHODS FOR ECONOMICS
Learning outcomes of the course unit
In an ever increasing number of contexts, it is advisable that a graduate student in
Economics is able to use quantitative measurements and tools. The main objective
of this course is to provide the student the basic mathematical instruments to
construct simple models for economic problems and take informed and justified
At the end of the course, the student
- understand and properly treat the main models
presented in the course;
- be able to analyze, formalize and solve practical (economical) problems;
- show good skills in making judgement;
- clearly communicate what he/she has learned using an appropriate language.
First and second order equations and inequalities. Properties of exponentiation.
Course contents summary
Linear functions and models. Linar systems and matrices. Economic applications.
Differential Calculus and economic applications.
Integrals. Functions in several variables. Economic applications.
Real functions. Graph of a function.
Linear functions and models. Economic applications.
Systems of linear equations.
Linear algebra: vectors and matrices.
Non-linear models: quadratic functions, exponential functions, logarithm.
Limits and continuity of functions. First and second derivatives.
Maxima and minima of functions.
Integration theory: indefinite and definite integral. Fundamental theorem of calculus.
Integration by parts and by substitution.
Introduction to functions of several variables. Partial derivatives of first and second
order. Hessian matrix.
Maxima and minima of functions of two variables.
Constrained optimization:Lagrange's multipliers.
S. Waner, S.R. Costenoble, Strumenti quantitativi per la gestione aziendale,
Maggioli Editore, 2018
During the classes, a theoretical exposition of the contents of the course will be
Then, a great number of examples and exercises will be discussed, with a particular
focus on economic applications. The students will be asked to discuss and propose
possible solutions to the exercises.
On the Elly platform the detailed program and the exams of the previous years will be uploaded at the beginning of the course. To download the material, registration to the online
course is required
Assessment methods and criteria
During the exam, the student can use a scientific
calculator. Graphic calculators, smartphone, tablet,
laptops and smartwatch are not allowed.
The knowledge and the skill in comprehension will
be tested through three questions about elementary
mathematics (1), a problem (2) and three theoretical
The quality of learning, the skill in the applications of
and the independence of judgement will be verified
through the economic problem (2). In order to solve
such a problem, the student will individuate an
opportune mathematical model, by obtaining the
solution through the analytical tools presented in
The use of an appropriate technical language will be
checked through three open questions (3) about the
theoretic subjects of the Course.
If the exam is excellent (for completeness,
brightness and organization of the answers,
concepts not specifically treated in the course), it is
valuated with full marks cum laude.
The teacher reserves the right to complete the exam
with an oral test, if
Results will be communicated to the students within 10 days, via Esse3. The solution of the exam will be uploaded on the Elly platform within 7 days.