JEM096 - Economic Dynamics I
| Credit: | 6 |
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| Credit ETCS: | 6 |
| Hours weekly: | 2/2 |
| Status: | Anglicky EEI a HP - povinně volitelný ET - povinně specializační F,FT a B - povinně volitelný Magisterský - vše MEF - elective Semestr - zimní |
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| Course supervisors: | prof. Ing. Miloslav Vošvrda CSc. |
| Teachers: | prof. Ing. Miloslav Vošvrda CSc. |
| Assistants: | PhDr. Jaromír Baxa Ph.D. Ing. Aleš Maršál M.A. Mgr. Josef Stráský |
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| Literature: | Ronald Shone: Economic Dynamics: Phase Diagrams and their Economic Application, Cambridge University Press, 2003 Ronald Shone: An Introduction to Economic Dynamics, Cambridge University Press, 2001 Chiang, Alpha C.: Fundamental Methods of Mathematical Economics. McGraw-Hill, 3rd ed. (or newer). Dawkins, Paul: Differential Equations – Lecture notes available here: http://tutorial.math.lamar.edu/ (follow the link to Differential Equations (Math 3301) link). Day, Richard H.: Complex Economic Dynamics. MIT Press, vol. 1 1995, vol. 2, 2000. (Chapters 1-5 of the first volume are related o this course). Hájková, John, Kalenda, Zelený: Matematika, Matfyzpress, Praha 2006 Software Used: Mathematica MS Excel |
| Description: | The course is focused on mathematical methods which are underlying modern economic theory such as difference and differential equations and their systems, dynamic optimization methods, foundations of nonlinear dynamics and approximation methods such as linearization and log-linearization. Developed mathematical tools are used in solving important economic models such as IS-LM model or Ramsey model. Students will frequently use mathematical software as a solution tool. Moodle Site: http://dl1.cuni.cz/course/view.php?id=2709 |
| Content: | I. Introduction to the course II. Differential equations and their solutions – Continuous systems First order and second-order differential equations Solution methods, phase diagrams, direction field Solution in Mathematica III. Difference equations - Discrete systems First order and second-order difference equations Solution methods, phase diagrams. Solution in Maxima IV. Applications of difference and differential equations Harrod-Domar model Solow model Multiplier–Accelerator model Cobweb model V. Systems of differential and difference equations Definition and matrix notation Eigenvalues and eigenvectors Solutions methods of system of two differential equations Equilibrium Types of equilibrium: nodes, spirals and saddles Stability and instability VI. Applications of systems of difference and differential equations IS-LM model Dornbusch open economy model with flexible prices Overlapping generations models VII. Introduction into nonlinear dynamics Nonlinear differential and difference equations. Deterministic chaos Bifurcations Dynamics of Keynesian model with nonlinearities Endogenous cycle models. VIII. Dynamic Optimization Hamiltonian. The maximum principle of Pontryagin: continuous model. The maximum principle of Pontryagin: discrete model Dynamic optimization with discounting - Ramsey model. IX. Approximaton methods Taylor series. Linearization, log-linearization. X. Road to DSGE models |
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| Course requirements: | 6 problem sets (60%), final test (40%) |
| Downloadable: | 01_intro |