The aim of studying and bibliography

The main aim of study: Introduction of fundamental problems of mathematical economics. The structuring and solving mathematical models of economy.

The general information about the module: Mathematical theory of demand. Production theory. Market equilibrum and company equilibrum. Short and long periodic strategy of company. Functions and economic models. Linear models (IS-LM or supply-demand system). Growth models. Univariate optimization. Constrained optimization. Risk and uncertainty in the economics.

Bibliography required to complete the module

Bibliography used during lectures

1	S. Kanas	Podstawy ekonomii matematycznej	PWN Warszawa.	2011
2	E. Panek	Ekonomia matematycznaI	Wydawnictwo AE Poznań.	2000
3	Alpha Chiang	Fundamental Methods of Mathematical Economics	McGraw Hill.	1990

Bibliography used during classes/laboratories/others

1	S. Kanas	Podstawy ekonomii matematycznej	PWN Warszawa.	2011
2	E. Panek	Podstawy ekonomii matematycznej	Wydawnictwo AE Poznań.	2000
3	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	WN PWN, wydanie 9,.	2012

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: system of linear equations. Vectors, vector space. Properties of functions of one and several real variables, derivatives, extrema, differential equations.

Basic requirements in category skills: student solve systems of linear equations, student is able to determine the derivatives and local extrema of functions of one and several variables, solve differential equations.

Basic requirements in category social competences: student has a cognizance of the level of its knowledge and abilities, and cognizance of its shortcoming, that endeavours in a process of study.

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	The student knows the basic concepts of marginal calculus for functions of one variable, knows the examples of applications of differential equations in building economic models	lecture, exercices	test, written exam	K_W03+ K_U01+ K_K01+	P6S_KK P6S_UK P6S_WG P6S_WK
02	The student knows the basic concepts of the theory of preferences, preference relations, a budget set, optimal basket, autility function, elasticities of substitution and complementarity	lecture, exercices	test, written exam	K_K03+	P6S_KO P6S_KR
03	is able to apply the marginal calculus for the function of many variables, the utility function, the production function	lecture, exercices	test, written exam	K_W03+ K_K01+	P6S_KK P6S_WG P6S_WK
04	Knows the basic methods for solving nonlinear programming problems, the problem of utility maximization or minimization of costs	lecture, exercices	test, written exam	K_W03+ K_U36+ K_K03+	P6S_KO P6S_KR P6S_UK P6S_UO P6S_UU P6S_UW P6S_WG P6S_WK
05	Determines the marginal values for the demand function and supply function. Distinguishes between the concept of normal and Giffen goods, goods of lower and higher order, substitute and complementary goods	lecture, exercices	test, written exam	K_K03+	P6S_KO P6S_KR
06	Knows the basic models of market equilibrium	lecture, exercices	test, written exam	K_K03+	P6S_KO P6S_KR

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
6	TK01	Basic concepts of marginal calculus, the average function, flexibility of the function, the growth rate. Example for a function of the cost of production, a function of revenue, profit function, development of the population, demand, capital appreciation over time.	W01, W02	MEK01
6	TK02	The concept of a budget set and its response to price changes, budget, taxation, promotion.	W04	MEK02
6	TK03	The relation of preference, indifference curve, the set budget. Examples of preference relations: Cobb-Douglas, substitution, complementarity. The optimal basket on the budget line. Utility function, the properties of the utility function, the Gossen law.	W05, W06	MEK02
6	TK04	Economic characteristic function of many variables: for each variable (marginality, flexibility), with respect to two variables (substitution), with respect to the vector of variables	W07, W08	MEK03
6	TK05	Local extrema of functions of several variables, reminder and/or supplement. Global extremes in the convex areas. The utility maximization problem, the cost minimization problem	W09, W10, W11	MEK04
6	TK06	Marginal calculus of vector functions on the example of the demand function. Normal and Giffen goods, substitution and complementary goods, luxury and necessity goods	W12, W13	MEK05
6	TK07	Different approaches to the theory of Economic equilibrium. Linear and nonlinear models. A simple model of exchange.	W14, W15	MEK06

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 6)	The preparation for a test: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 3.00 hours/sem. Studying the recommended bibliography: 2.00 hours/sem.
Class (sem. 6)	The preparation for a Class: 3.00 hours/sem. The preparation for a test: 10.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 2.00 hours/sem.
Advice (sem. 6)		The participation in Advice: 1.00 hours/sem.
Exam (sem. 6)	The preparation for an Exam: 10.00 hours/sem.	The written exam: 1.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	written exam. MEK03-MEK06, the total number of points 100. The final evaluation is based on the number of points: 3.0 when obtained 50 - 60 p., 3.5 when obtained 61 - 74 p., 4.0 when obtained 75 - 82 p., 4.5 when obtained 83 - 91, 5.0 when obtained 92 - 100 pkt.
Class	test, MEK01-MEK03, number of points 80 and up to 20 points for their active participation in lectures and classes. The final evaluation is based on the number of points: evaluation 3.0 when obtained 50 - 60 p., evaluation 3.5 when obtained 61 - 74 p., evaluation 4.0 when obtained 75 - 82 p., evaluation 4.5 when obtained 83 - 91, evaluation 5.0 when obtained 92 - 105 p.
The final grade	medium from the evaluation of classes and exam with preference for evaluation of exam

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: no