MATHEMATICS FOR ECONOMICS

International Teaching MATHEMATICS FOR ECONOMICS

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8861200006
DEPARTMENT OF ECONOMICS AND STATISTICS
Corso di Dottorato (D.M.226/2021)
ECONOMICS AND POLICY ANALYSIS OF MARKETS AND FIRMS
2023/2024



Objectives
THE MAIN FOCUS OF THE COURSE IS TO INTRODUCE AND DEVELOP ANALYTICAL TOOLS GENERALLY USED IN THEORETICAL AND APPLIED ECONOMICS AND FINANCE. THE COURSE COVERS LINEAR ALGEBRA, FUNCTIONS OF SEVERAL VARIABLES AND OPTIMISATION WITH SEVERAL VARIABLES AND CONSTRAINTS. THE EDUCATIONAL GOAL OF THE COURSE IS TO PROVIDE STUDENTS WITH A GENERAL UNDERSTANDING OF THE MATHEMATICAL OBJECTS USED IN ECONOMICS IN ORDER TO FIND EFFICIENT METHODS FOR SOLVING PROBLEMS, BOTH ABSTRACT AND CONCRETE, IN UNCONSTRAINED AND CONSTRAINED OPTIMIZATION USING OPTIMIZATION METHODS IN A STATIC CONTEXT. THE COURSE ENABLES STUDENTS TO ACQUIRE THE KNOWLEDGE TO APPROACH THE STUDY OF THE MAIN ECONOMIC PROBLEMS, USING THE TOOL OF OPTIMISATION TO FIND POSSIBLE SOLUTIONS. AS PREREQUISITES, STUDENTS ARE EXPECTED TO BE FAMILIAR WITH THE BASIC MATHEMATICAL CONCEPTS TAUGHT IN UNIVERSITY-LEVEL COURSES IN ECONOMICS. THE COURSE INTRODUCES STUDENTS TO A RANGE OF OPTIMISATION CONCEPTS AND TECHNIQUES FOR ECONOMICS AND FINANCIAL ECONOMICS THAT FORM THE BASIS OF ADVANCED COURSES IN ECONOMIC THEORY. THE OPTIMISATION CONCEPTS AND TECHNIQUES INTRODUCED WILL BE DERIVED FROM THE BASIC PRINCIPLES AND ASSUMPTIONS AS FULLY AS POSSIBLE, AND WILL BE ILLUSTRATED USING STANDARD APPLICATIONS FROM ECONOMICS. BY THE END OF THE COURSE, THE STUDENT WILL HAVE THE KNOWLEDGE AND SKILLS TO UNDERSTAND THE BASIC ELEMENTS OF OPTIMIZATION THEORY IN A STATIC FRAMEWORK; TO APPLY MATHEMATICAL METHODS AND TECHNIQUES THAT ARE FORMULATED IN ABSTRACT CONTEXTS TO CONCRETE ECONOMIC APPLICATIONS; TO BE ABLE TO READ, UNDERSTAND AND FORMULATE APPROPRIATE OPTIMIZATION PROBLEMS, USING APPROPRIATE MATHEMATICAL TERMINOLOGY. STUDENTS WILL BE ABLE TO LEARN THE MAIN THEORETICAL RESULTS AND PRACTICAL METHODS RELATED TO OPTIMIZATION PROBLEMS THAT CAN DESCRIBE THE BEHAVIOUR OF AN ECONOMIC AGENT.
Prerequisites
PARTICIPANTS SHOULD BE FAMILIAR WITH
- 1ST AND 2ND MODULES: KNOWLEDGE OF BASIC MATHEMATICS TAUGHT IN GRADUATE-LEVEL COURSES IN ECONOMICS
Contents
1ST MODULE: CALCULUS OF SEVERAL VARIABLES AND OPTIMIZATION (5H)
UNIT 1 – POINTS AND VECTORS IN EUCLIDEAN SPACE
UNIT 2 – CALCULUS OF SEVERAL VARIABLES
UNIT 3 – THE TOTAL DERIVATIVE AND HIGHER-ORDER DERIVATIVES
UNIT 4 – QUADRATIC FORMS AND DEFINITE MATRICES
UNIT 5 – UNCONSTRAINED OPTIMIZATION

2ND MODULE: CONSTRAINED OPTIMIZATION AND LINEAR INDEPENDENCE (5 H)
UNIT 1 – CONSTRAINED OPTIMIZATION AND FIRST ORDER CONDITIONS
UNIT 2 – CONSTRAINED OPTIMIZATION AND SECOND ORDER CONDITIONS
UNIT 3 – CONCAVE E QUASICONCAVE FUNCTIONS

Teaching Methods
FRONTAL LESSONS
Verification of learning
THE ACHIEVEMENT OF THE OBJECTIVES OF THE COURSE IS VERIFIED BY PROJECT WORK.
Texts
MATHEMATICS FOR ECONOMISTS BY CARL P. SIMON AND LAWRENCE BLUME.
More Information
FOR FURTHER INFORMATION PLEASE CONTACT GBIMONTE@UNISA.IT AND MRUSSOLILLO@UNISA.IT
  BETA VERSION Data source ESSE3