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Mathematics in Economics

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Course Unit Code151-0335/02
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
SED02doc. Ing. Petr Seďa, Ph.D.
Summary
This course connects the existing knowledge of mathematics and economics obtained at bachelor level of study so that students apply the knowledge of mathematics in the area of microeconomics and macroeconomics. The aim of this course is to enable students to understand the benefits of using mathematics as a very useful tool for understanding objective economic reality using mathematical abstraction. Students should discover connections and relationships by comparing economic phenomena having different content but same formal description. This approach allows students to achieve a deeper knowledge of economics.
Learning Outcomes of the Course Unit
The main aim of the course is to teach students how to use mathematics effectively and to increase knowledge and understanding of microeconomic and macroeconomic problems.
Students will get the following knowledge, skills and abilities:
• will be able to use mathematics as a tool for deeper understanding of microeconomics and macroeconomics,
• will be able to study economics effectively,
• will learn how to apply methods and procedures of mathematical analysis to solve practical economic problems at the microeconomic and macroeconomic level,
• will be able to describe solutions of selected economic problems using mathematical tools, check individual steps of given solution, generalize conclusions and evaluate the correctness of results with respect to given conditions.

Course Contents
1. Introduction.
Mathematical modelling in economics. Classification of economic and mathematical models. Functional dependency.
2. Approximation of real functions.
Interpolation by algebraic polynomials. Lagrange interpolation method. Approximation by the least squares method.
3. Differential calculus of functions of one variable in economic applications.
Economic functions and their properties, the slope of a function. Total, average and marginal variables in economics, elasticity of a function.
4. Differential calculus of multivariable functions in economic applications I.
The methods of optimizing the multivariable functions in economics - the substitution method, the method of Lagrange multipliers, the method of comparison of marginal rates of substitutions.
5. Differential calculus of multivariable functions in economic applications II.
Constrained extrema of multivariable functions in economics. Model with multiply inputs. Evaluation of efficiency.
6. Differential calculus of multivariable functions in economic applications III.
The methods of optimization in imperfect models markets.
7. Integral calculus in economics.
Application of definite and indefinite integrals in economics. Flow quantities in economics and their accumulation over time.
8. Functional dependence as a tool for modelling static economic phenomena.
Models of static equilibrium. Models of comparative statics in economics.
9. Mathematical basis of discrete linear dynamic models in economics I.
Difference equation – a mathematical tool for modelling the discrete macroeconomic dynamic processes in economics.
10. Mathematical basis of continuous linear dynamic models in economics I.
Analogy of discrete and continuous models. Differential equations - a mathematical tool for modelling the continuous macroeconomic dynamic processes in economics.
11. Mathematical basis of discrete linear dynamic models in economics II.
Difference equations - mathematical tool for modelling the discrete microeconomic dynamic processes in economics.
12. Mathematical basis of continuous linear dynamic models in economics II.
Differential equations – a mathematical tool for modelling the continuous microeconomic dynamic processes in economics.
Recommended or Required Reading
Required Reading:
DOWLING, Edward T. Schaum's Outline of Introduction to Mathematical Economics. New York: McGraw-Hill, 2011. 552 s. ISBN 978-0071762519.
KLEIN, Michael. Mathematical Methods for Economics. London: Pearson College, 2019. 580 s. ISBN 978-0201726268.
MAVRON, Vassilis a Timothy PHILLIPS. Elements of Mathematics for Finance. London: Springer, 2007. 322 s. ISBN 978-3-540-05117-6.

FIALA, Petr. Základy kvantitativní ekonomie a ekonomické analýzy. Praha: Vysoká škola ekonomická v Praze, 2006. 165 s. ISBN 80-245-1087-1.
KLEIN, Michael. Mathematical Methods for Economics. London: Pearson College, 2019. 580 s. ISBN 978-0201726268.
MEZNÍK, Ivan. Úvod do matematické ekonomie pro ekonomy. Brno: CERM, 2017. 190 s. ISBN 978-80-214-5512-2.
Recommended Reading:
CHIANG, Alpha a Kevin WAINWRIGHT. Fundamental Methods of Mathematical Economics. New York: McGraw-Hill/Irwin, 2004. 704 s. ISBN 0-07-066219-3.
SYDSAETER, Knut a Peter HAMMOND. Essential Mathematics for Economic Analysis. London: Pearson College, 2008. 721 s. ISBN 978-0273713241.
YU Kam. Mathematical Economics: Prelude to the Neoclassical Model. Heidelberg: Springer, 2019. 227 s. ISBN 978-3030272913.
BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK a Vít MIKULÍK. Matematika v ekonomii a ekonomice. Praha: Grada Publishing, 2015. 352 s. ISBN 978-80-247-4419-3.
MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. Praha: Grada Publishing, 2015. 272 s. ISBN 978-80-247-5406-2.
PRAŽÁK, Pavel. Diferenční rovnice s aplikacemi v ekonomii. Hradec Králové: Gaudeamus, 2013. 375 s. ISBN 978-80-7435-268-3.
Planned learning activities and teaching methods
Lectures, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Graded creditGraded credit100 (100)51
        Test 1Written test50 26
        Test 2Written test50 26