Course detail

# Mathematical modeling

FP-KmmPAcad. year: 2018/2019

The subject is focused on precise mathematical formulation of economic models and at the same time appropriate economic interpretation of these models.

Supervisor

Department

Learning outcomes of the course unit

Objective of the course - learning outcomes and competences: Students will be able to understand and describe solutions of selected economic problems using previous and newly acquired knowledge of mathematical,

The student is able to apply both existing and newly acquired mathematical knowledge in solving selected economic problems

Prerequisites

Basic knowledge of Mathematics 1 and 2: properties of numbers, derivative, integral, function of one variable, function analysis of two variables
Basic knowledge of microeconomics and macroeconomics.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

MEZNÍK, I. Úvod do matematické ekonomie pro ekonomy. 2. vyd. Brno: CERM, s.r.o., 2017. 189 s. ISBN 978-80-214-5512-2. (CS)

PRAŽÁK, P. Diferenční rovnice s aplikacemi v ekonomii. Hradec Králové: Gaudeamus, 2013. 360 s. ISBN 978-80-7435-268-3.

GROS, I.; DYNTAR, J. Matematické modely pro manažerské rozhodování. 2. upravené a rozšířené vyd. Praha: Vysoká škola chemicko-technologická v Praze, 2015. 303 s. ISBN 978-80-7080-910-5.

BUTCHER, J. C. (John Charles). Numerical methods for ordinary differential equations. Third edition. Chichester: Wiley, 2016. 513 s. ISBN 978-1-119-12150-3.

CHIANG, A. C.; WAINWRIGHT, K. Fundamental methods of mathematical economics. 4th ed. Boston: McGraw-Hill/Irwin, 2005. 688 s. ISBN 0-07-010910-9.

Planned learning activities and teaching methods

The lectures are in the form of lectures which have the character of interpretation of basic principles, methodology of given discipline and problems. The main emphasis is put on explaining the essence of each method and its general characteristics.

Assesment methods and criteria linked to learning outcomes

The form of the exam is written and the teacher reserves the right to the oral examination. The maximum number of points in the exam is 100 points, and the student must earn at least 50 points in order to obtain a rating of at least E..

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

The course focuses on the precise mathematical formulation of economic models and the appropriate economic interpretation of these models. Upon successful completion of this course, students will be able to use mathematics as a tool for deeper understanding of economics and apply acquired mathematical knowledge in solving selected economic problems.

1. Mathematical modeling in economics. Classification of economic-mathematical models.

2. Mathematical modeling in economics - basic mathematical means for exploring functions in economics.

3. Interpolation and function approximation. Interpolation with algebraic polynomials. Lagrange interpolation method. Approximate least squares method.

4. Mathematical Analysis of Selected Economic Addictions - Consumer Decision Making.

5. Mathematical analysis of selected economic dependencies - production model with multiple inputs.

6. Methods of mathematical analysis and mathematical programming. Models of imperfect markets. Evaluation of production efficiency.

7. Flow variable in economy - investment and accumulation of capital. Analysis of selected economic functions.

8. Functional dependence as a tool for modeling macroeconomic phenomena. Static equilibrium models. Static concept of multiplier, accelerator. Mathematical derivation of the IS-LM model.

9. Mathematical basis of continuous dynamic models in economics. Analogue Discrete and Continuous Models. Differential equations as a tool for modeling continuous macroeconomic dynamic processes.

10. Differential equations as a tool for modeling of continuous microeconomic dynamic processes.

11. Mathematical basis of discrete dynamic models in economics. Differential equations as a tool for modeling discrete macroeconomic dynamic processes.

12. Differential equations as a tool for modeling discrete microeconomic dynamic processes.

13. Application of differential and differential equations in selected microeconomic models. Continuous and discrete models in logistics.

Aims

Learning outcomes of the course unit The aim of the course is to acquaint students with models of mathematical economics and economic models using mathematical apparatus and with precise mathematical formulation in the field of economic models and at the same time appropriate economic interpretation of these models.

Specification of controlled education, way of implementation and compensation for absences

Attendance at lectures is optional.

Classification of course in study plans

- Programme BAK-EP Bachelor's, 2. year of study, winter semester, 3 credits, compulsory-optional