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 will be able to analyze and formalize some
economic problems. In particular, she/he will be able to identify the data of the
problem and to construct the most suitable model, choosing the appropriate
mathematical methods to solve the problem in an efficient and rigorous way. The
student will also be able to give an economic interpretazion to the results of her/his
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,
Apogeo, Milano, 2006
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.
Assessment methods and criteria
The acquisition of knowledge and understanding will be tested by 3 questions about
the prerequisites, a problem and 3 questions about the theory.
In particular, 3 initial questions (1 pt each) will be used to test the mastery of the
preliminary notions required for the course.
To evaluate the learning ability, the capacity of applying the learned concepts to real
problems and the independence of judgement, a problem (value: 15 pt.)will be
proposed to the student, who must choose the appropriate mathematicalmodel and
method to find a solution and interpret the obtained results.
The acquisition of a technical language will be evaluate through 3 questions (4 pt.
each) on theoretical topics covered in the course.
An additional oral exam may be required by the teacher.