JEM096 - Economic Dynamics I
EEI a HP - povinně volitelný
ET - povinně specializační
F,FT a B - povinně volitelný
Magisterský - vše
MEF - elective
Semestr - zimní
|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
|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
|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
V. Systems of differential and difference equations
Definition and matrix notation
Eigenvalues and eigenvectors
Solutions methods of system of two differential equations
Types of equilibrium: nodes, spirals and saddles
Stability and instability
VI. Applications of systems of difference and differential equations
Dornbusch open economy model with flexible prices
Overlapping generations models
VII. Introduction into nonlinear dynamics
Nonlinear differential and difference equations.
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
X. Road to DSGE models
|Course requirements:||6 problem sets (60%), final test (40%)|