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Main menu for Browse IS/STAG
Course info
KMA / MAE
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Course description
Department/Unit / Abbreviation
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KMA
/
MAE
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematical Economics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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|
|
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Automatic acceptance of credit before examination
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No
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Summer semester
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13 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The purpose of this course is to get students acquainted with basic principles of the mathematical economics. We deal with tools arising mainly from static decision theory and the game theory. The focus lies on mathematical formulation of standard micro- and macroeconomic models. Consequently, their properties and economic interpretations are discussed.
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Requirements on student
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Assignments during semester. Final examination consists of written and oral parts.
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Content
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1. Specifics of mathematical economics. Classification of variables.
2. Decision theory. Optimization vs. game theory. Actions, strategies, behaviour.
3. Static games. Dominance.
4. Nash equilibirum. Best response function. Zero-sum games.
5. Dynamic games. Empirical economics (discrete ultimatum).
6. Mixed games. Market entrance models.
7. Discounting theory. Repetition. Time inconsistency.
8. Continuous approximations. Duopoly, oligopoly models.
9. Collective cooperation. Externalities. Pigou tax.
10. Mechanism design. Moral hazard. Auction theory.
11. Evolutionary stable strategies.
12. Replicator dynamics. Market saturation models.
13. Reserve.
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Activities
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Fields of study
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Studentům je k dispozici kurz v Google Classroom se všemi podstatnými informacemi a materiály.
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Guarantors and lecturers
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-
Guarantors:
Doc. RNDr. Petr Stehlík, Ph.D. (100%),
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Lecturer:
Doc. RNDr. Petr Stehlík, Ph.D. (100%),
RNDr. Vladimír Švígler, Ph.D. (100%),
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Tutorial lecturer:
Doc. RNDr. Petr Stehlík, Ph.D. (100%),
RNDr. Vladimír Švígler, Ph.D. (100%),
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Literature
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Basic:
Webb J. Game Theory. 2007.
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Basic:
Matematická ekonomie - poznámky k přednáškám
(Stehlík P.)
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Recommended:
Vohra, Rakesh V. Advanced mathematical economics. London : Routledge, 2005. ISBN 0-415-70008-6.
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Recommended:
Fudenberg D., Tirole J. Game Theory. MIT Press, 1991. ISBN 0-262-06141-4.
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Recommended:
Baldani, J. - Brandfield, J. - Turner R. W. Mathematical Economics. South-Western College Pub, 2nd Edition, 2004.
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Recommended:
Angel de la Fuente. Mathematical Methods and Models for Economists. Cambridge University Press. ISBN 0521585295.
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Recommended:
Klein, M. Mathematical Methods for Economics. Addison Wesley, 2nd Edition.
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Recommended:
Zimmermann, K. Úvod do matematické ekonomie. Praha Karolinum, 2002.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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40
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Contact hours
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60
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Individual project (40)
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40
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Total
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140
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
rozumět základům diferenciálního počtu (v rozsahu KMA/MA1) |
rozumět základům integrálního počtu (v rozsahu KMA/MA1) |
rozumět základům lineární algebry (v rozsahu KMA/LAA) |
rozumět základům funkcí více proměnných (v rozsahu KMA/MA2) |
rozumět základům teorie grafů (v rozsahu KMA/DMA) |
rozumět základům teorie pravděpodobnosti (v rozsahu KMA/PSA) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
najít extrémy funkce jedné reálné proměnné |
ovládat operace s maticemi |
umět načrtnout vrstevnice a najít extrémy funkcí více proměnných |
určit základní charakteristiky diskrétních i spojitých rozdělení |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
rozumět specifickým vlastnostem matematické ekonomie a proměnných, které se v ní vyskytují, včetně jejich klasifikace |
vysvětlit význam diskrétních struktur v matematické ekonomii |
popsat rozdíl mezi klasickou optimalizací a teorií her |
rozumět principům základních statických mikro a makroekonomických modelů zejména z pohledu teorie her |
vysvětlit význam vzorových příkladů v teorii her a zavedení různých typů rovnováh |
vysvětlit rozdíl mezi statickými, dynamickými hrami, hrami s opakováním, kolektivními hrami a hrami proti poli |
Skills - skills resulting from the course: |
nalézt řešení základních optimalizačních úloh |
nalézt čisté i smíšené Nashovy rovnováhy statických her |
umět konstruovat dynamické hry a nalézt Nashovu rovnováhu vzhledem k podhrám pomocí zpětné indukce |
vyřešit matematické modely monopolu a různých duopolistických modelů |
rozumět pojmu evoluční stability a umět ji určit pomocí replikátorových rovnic |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Interactive lecture |
Seminar |
Task-based study method |
Textual studies |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Interactive lecture |
Practicum |
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