Mathematical methods in dynamic economics / András Simonovits.

Format:

Book

Author/Creator:

Simonovits, András.

Language:

English

Subjects (All):

Economics, Mathematical.

Statics and dynamics (Social sciences)--Mathematical models.

Statics and dynamics (Social sciences).

Physical Description:

x, 317 pages : illustrations ; 23 cm

Place of Publication:

New York : St. Martin's Press, 2000.

Summary:

This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete -- as well as continuous -- time systems, linear, and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-derived multicohort economy.

Contents:

1. Linear Difference Equations. 1.1. Difference equations. 1.2. General linear systems. 1.3. Planar linear systems. 1.4. Linear control systems

2. Discrete-Time Linear Models. 2.1. Linear model of accelerator-multiplier. 2.2. Linear models of control by stock signals. 2.3. Linear decentralized control with expectations

3. Nonlinear Difference Equations. 3.1. Existence and stability of fixed points. 3.2. Limit cycles. 3.3. Chaos

4. Discrete-Time Nonlinear Models. 4.1. Irregular growth cycles. 4.2. Nonlinear models of accelerator-multiplier. 4.3. Nonlinear model of control by stock signals. 4.4. Nonlinear stock control with expectations. 4.5. Mixed expectations. 4.6. Related issues

5. Ordinary Differential Equations. 5.1. Basic concepts and theorems. 5.2. Linear systems. 5.3. Nonlinear systems. 5.4. Control in continuous time

6. Continuous-Time Models. 6.1. Growth models. 6.2. Government stabilization. 6.3. Competitive price adjustment

7. Dynamic Programming. 7.1. Deterministic principle of optimality. 7.2. Stochastic principle of optimality. 7.3. Optimal LQ control with perfect observation. 7.4. Optimal LQG control with imperfect observation

8. Applications of Dynamic Programming. 8.1. Optimal saving. 8.2. One-sector optimal accumulation. 8.3. Multisector optimal accumulation. 8.4. The great fish war

9.

Optimal Control. 9.1. Basic problem. 9.2. Calculus of Variations. 9.3. Supplements

10. Optimal Consumption Paths. 10.1. Exogenous wage and interest. 10.2. Endogenous wage and interest: infinite horizon. 10.3. Constant capital-output ratio: finite horizon. App. A. Linear Algebra

App. B. Overlapping Generations

App. C. Overlapping Cohorts.

Notes:

Includes bibliographical references (pages 295-309) and index.

ISBN:

0333778189

0312229402

OCLC:

42080193