JEM096 - Economic Dynamics I

Credit: 6
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
Obligatory courses:
Recommended courses:
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
Schedule:
Announcements:
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
Seminar:
Examination dates:
Course requirements: 6 problem sets (60%), final test (40%)
Downloadable: 01_intro