MPE_MAMI Mathematical Microeconomics

Faculty of Economics and Administration
Autumn 2010
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Dalibor Moravanský, CSc. (lecturer)
RNDr. Dalibor Moravanský, CSc. (seminar tutor)
Guaranteed by
RNDr. Dalibor Moravanský, CSc.
Department of Economics – Faculty of Economics and Administration
Contact Person: Lydie Pravdová
Timetable
Wed 12:50–14:30 VT206
Prerequisites
! PMMEK Mathematical Economics
From a student of PMMEK, knowledge of following subjects is required: Mathematics I,II,Statistics I,II,Microeconomics,Macroeconomics
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course of Mathematical Economics comprises several (usually 4) important parts of formalized economic theory, which can be expressed by means of advanced mathematic tools. The main attention is given to the rigorous analysis of economic relations in the two following areas: modelling of rational behavior of the producer, and the analysis of optimum behavior of the consumer, which is, in detail, studied in utility theory. The exposition relating two other important economic topics - principles of the construction of "reasonable" index numbers and foundations of modelling of economic growth (with a limited number of macro-economic variables) - follows. Marginally, the problem of aggregation of micro-economic variables and relations into appropriate macro-economic aggregates is discussed. By passing the course, its attendant becomes sufficiently qualified to be able, alone or in specialized courses, to continue the study of selected themes of mathematical economy on a higher level and be able to study the literature from this area (the highest level is represented by the Econometrica magazine). The student also becomes acquainted with many terms of theoretic economics that can be expressed precisely by mathematic tools (e.g. with the help of differential calculus). Finally, the student gains, in selected areas (index numbers and production theory), the necessary theoretical point of view, which does not use some naive tools, which, in some areas (e.g. indices of the financial markets or measuring of inflation), are still used in economic or statistical practice. The teaching emphasis is laid primarily on: - understanding of the purpose of the rigorous mathematical formulation of the economic tasks and their solution. - appropriation of these economic notions, which may be rationally described by mathematic means. - ability to distinguish a tolerable rate of simplification of the model compared to economic reality. - reinforcement of exact aspects over intuitive features when working with economic notions and relations.
Syllabus
  • 1. Index numbers: Purpose, notation, history, persons, approaches, main application areas. Basic types of means: arithmetic, geometric, harmonic, quadratic. General mean of order r. The ways and importance of choice of weights. Axiomatic/test approach of I.Fisher: introduction of tests, verification, interpretation. 2. Index numbers: Classical approaches to index number construction: Carli/Sauerbeck, Laspeyres, Paasche, Jevons, Edgeworth, Walsh, Fisher, Bowley. Interpretation as weighted averages, Schlomilch inequality, Bortkiewicz ratio: formulation, derivation, consequences. Walsh suggestion. 3. Index numbers: Further approaches to IN construction: chaining: importance, definition, purpose, generalization. Gini's and Stuvel's IN: starting points, construction, discussion. Outline of the Divisia's general approach to discrete and continuous situations. 4. Consumer theory: Measuring of utility, utility function: Preference relation and its basic properties, requirements for considering of the consumer. Transfer from the preference relation to the utility function. Properties of the utility function, the U-matrix (of the first and second partial derivatives of the utility function). 5. Consumer theory: Marginal utility, marginal rate of substitution. Monotone transformation of the utility function relative to the |U| determinant. Formulation of the primary optimization problem of consumer behavior. Necessary and sufficient (Hicks's) conditions for the extremum. Dual (minimization) problem. 6. Consumer theory: Mathematical derivation of the income and substitution effects, classification of commodities (substitutes, complements) according to the behavior at changing income and prices. Consequences for different commodity types. Compensated change of the demand and its impacts. Giffen's effect. Generalization for more commodity groups. 7. Consumer theory: Expenditure function and its properties. Indirect utility function and its properties. Shephard lemma and Roy identity – formulation, purpose. Marshallian and Hicksian demand functions and its properties. Engel and Cournot aggregation conditions. 8. Theory of production: Basic notions,formalization of the problem. Production function: technology, output, production factors. Production input set, isoquant, efficient subset. Shephard's axioms for the production function–verification, examples: Cobb-Douglas, ACMS, Leontieff, flexible functional forms. 9. Theory of production: Basic economic characteristics of the production function: marginal products, factor shares, elasticity of output to the production factor, marginal rate of substitution, returns to scale, homogeneity. Elasticity of substitution and computing expressions: general, simplified. Euler's theorem. 10. Theory of production: Further economic properties of the pr.f.: Substitutionality, limitationality, essentiality. Cost function and its properties, revenue function and its properties. Optimization criteria for choosing the optimum size of production. Profit function and its properties, symmetry. Hotelling lemma. 11. Economic growth models: Purpose, classification, used macroeconomic variables, relations. Simplifications. Mathematical formulations: equilibrium, multiplier, accelerator. Elements of the macro-economic model: consumption function, investment function, income identity. Model of the static multiplier. Model of the dynamic multiplier. Equilibrium income trajectory. 12. Economic growth models: Harrod-Domar theory of the economic growth (at the continuous case): Diversity of the income trajectories at different types of autonomous investment: constant, linear, exponential. Mathematical solutions of the different cases. 13. Economic growth models: Phillips (continuous) multiplier model: formulation, solution, shapes of resulting trajectories. Phillips(continuous) multiplier-accelerator model. Formulation and complete solution of the differential equation of the 2nd order. Analysis of variants of income trajectories depending on parameters of the model. Samuelson-Hicks (discrete) growth model. Discussion.
Literature
  • CORNES, R. Duality and Modern Economics. Holland: North Holland P.C., 1992. info
  • ALLEN, R. G. D. Matematická ekonomie. Translated by Martin Černý. Vyd. 1. Praha: Academia, 1971, 782 s. URL info
Teaching methods
lectures
Assessment methods
The course is in a traditional form with audio-visual support. The written part of the exam lasts 90 minutes and usually consists of 7 tasks. To pass the exam it is necessary to achieve 55% score (11 points of the maximum of 20). The following oral part of the exam consists of a more detailed discussion of 1-2 problem topics.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Nezapisují si studenti, kteří absolvovali předmět PMMEK.
The course is also listed under the following terms Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013.
  • Enrolment Statistics (Autumn 2010, recent)
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