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# Instrumental Methods of Economic Analysis

2021/2022
ENG
Instruction in English
3
ECTS credits
Course type:
Bridging course
When:
1 year, 1 module

#### Instructor

Pokrovsky, Dmitry A.

### Course Syllabus

#### Abstract

The course consists of lectures (8 hours) and tutorials (16 hours). The tutorials involve studying calculus and linear algebra methods and their application to solving constrained and unconstrained optimization problems using terms and concepts studied in class.

#### Learning Objectives

• understanding the basic concepts of mathematical analysis and linear algebra
• acquiring skills in solving optimization problems of various types

#### Expected Learning Outcomes

• Be able to solve unconstrained and constrained optimization problems
• Have an understanding of the envelope theorem and be able to use it in the optimization problems
• Know the necessary and sufficient conditions for concavity/convexity of the function and maximum/minimum.
• Understand the theory of elementary functions, methods of calculus related to the differentiation of single and multiple variable functions.

#### Course Contents

• Linear algebra: operation with matrices, square matrices, determinant, eigenvalues and eigenvectors
• Functions of one variable: derivative of the function, necessary and sufficient conditions for increasing/decreasing, concavity/convexity, extremum and inflection points.
• Functions of multiple variables: first and second order partial derivatives, Schwarz theorem, necessary and sufficient conditions for concavity/convexity and extremum points
• Unconstrained optimization of multiple variables functions: necessary and sufficient conditions for local/global maximum/minimum, envelope theorem
• Constrained optimization of multiple variable functions. Equality constrains: necessary and sufficient conditions for maximum/minimum, relationship between concavity/convexity of the function with the type of extremum. Inequality constrains: Kuhn-Tucker theorem, relationship between concavity/convexity of the function with the type of extremum

• test 1
• test 3
• test 2

#### Interim Assessment

• 2021/2022 1st module
0.4 * test 3 + 0.3 * test 2 + 0.3 * test 1

#### Recommended Core Bibliography

• Sundaram, R. K. (1996). A First Course in Optimization Theory. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521497701