Dynamic economics : optimization by the Lagrange method / Gregory C. Chow.

Format:

Book

Author/Creator:

Chow, Gregory C., 1929-

Language:

English

Subjects (All):

Mathematical optimization.

Multipliers (Mathematical analysis).

Equilibrium (Economics).

Statics and dynamics (Social sciences).

Economic development.

Physical Description:

xiii, 234 p. : ill.

Edition:

1st ed.

Place of Publication:

New York : Oxford University Press, 1997.

Summary:

Gregory C. Chow, father of the Chow Test of stability of economic relations and a major contributor to econometrics and economics, here provides a unified and simple treatment of dynamic economics. Using dynamic optimization as his main theme, Chow introduces the Lagrange method as a more convenient tool than dynamic programming for solving dynamic optimization problems. Dynamic Economics presents the optimization framework for dynamic economics so that readers can understand and use it for applied and theoretical research. Chow shows how the method of Lagrange multipliers is easier and more efficient for solving dynamic optimization problems than dynamic programming, and so enables readers to grasp the substance of dynamic economics more fully. He employs the Lagrange method to study and solve problems in a variety of areas including economic growth, general equilibrium theory, business cycles, dynamic games, finance, and investment--while also discussing numerical methods and analytical solutions. Teaching by example, Chow solves simple problems before moving on to more general propositions. Problems are provided at the end of each chapter. This accessible and wide-ranging work is an ideal primary text for graduate and undergraduate courses in dynamic economics. It can also be used as a supplementary text for courses in mathematics for economists, mathematical economics, macroeconomics, economic development, finance, operations research, and control theory in engineering schools, among others.

Contents:

Intro

Contents

Chapter One: Introduction

1.1 Dynamic Economics and Optimization

1.2 Methods of Dynamic Optimization

1.3 Economic Growth

1.4 Theories of Market Equilibrium

1.5 Business Cycles

1.6 Dynamic Games

1.7 Models in Finance

1.8 Models of Investment

1.9 Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems

Chapter Two: Dynamic Optimization in Discrete Time

2.1 The Method of Lagrange Multipliers by an Example

2.2 The Method of Dynamic Programming by an Example

2.3 Solution of a Standard Dynamic Optimization Problem

2.4 Numerical Solution by Linear Approximations of &amp

#955

and g

2.5 Sufficient Conditions for a Globally Optimal Solution

2.6 Relations to Known Results on Optimization

Problems

Chapter Three: Economic Growth

3.1 The Brock-Mirman Growth Model

3.2 A Multisector Growth Model

3.3 A Growth Model Based on Human Capital and Fertility

3.4 Technology and Economic Growth

3.5 Research and Development and Economic Growth

Chapter Four: Theories of Market Equilibrium

4.1 Asset Prices of an Exchange Economy

4.2 Equilibrium in a Pure Currency Economy

4.3 A Pure Credit Economy with Linear Utility

4.4 Money and Interest in a Cash-In-Advance Economy

4.5 A One-Sector Model of General Equilibrium

4.6 Equilibrium of a Multisector Model

4.7 Equilibrium of a One-Sector Model with Tax Distortion

Chapter Five: Business Cycles

5.1 Keynes and the Classics

5.2 Dynamic Properties of a Multisector Model with Technology Shocks

5.3 Estimating Economic Effects of Political Events in China

5.4 Estimating and Testing a Base-Line Real Business Cycle Model

5.5 Real Business Cycles and Labor Market Fluctuations

5.6 Oligopolistic Pricing and Aggregate Demand.

5.7 Research on Real Business Cycles

Chapter Six: Dynamic Games

6.1 A Formulation of Models of Dynamic Games

6.2 Price Determination of Duopolists with No Consumer Switching

6.3 A Characterization of Subgame Perfect Equilibrium for Infinitely Repeated Games

6.4 A Characterization of Subgame Perfect Equilibrium for Dynamic Games

6.5 Credible Government Policy

6.6 Credible Taxation to Redistribute Income

Chapter Seven: Models in Finance

7.1 Stochastic Differential Equations

7.2 Dynamic Programming for a Continuous-Time Model

7.3 Solution of a Continuous-Time Optimization Problem by Lagrange Multipliers

7.4 An Algebraic Method for Finding the Optimal Control Function

7.5 Optimum Consumption and Portfolio Selection Over Time

7.6 Capital Asset Pricing with Shifts in Investment Opportunities

7.7 The Pricing of Options and Corporate Liabilities

7.8 Asset Pricing and Portfolio Selection with Noise in Supply

7.9 Asset Pricing and Portfolio Selection with Asymmetric Information

7.9a The Kalman Filter in Continuous Time

Chapter Eight: Models of Investment

8.1 Investment as Exercising an Irreversible Option to Invest

8.2 A Simple Model of Investment with Adjustment Cost

8.3 Investment as Gradual Capacity Expansion with Adjustment Cost

8.4 Optimal Policy for Replacement Investment

8.5 Optimal Policy to Retire Human Capital

8.6 Some Other Literature on Investment

Chapter Nine: Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems

9.1 Introduction

9.2 Change of Variables

9.3 A Short-Cut to Log-Linearize First-Order Conditions

9.4 Solving Matrix Riccati Equations Rapidly

9.5 Solving Linear First-Order Conditions by the Method of Undetermined Coefficients

9.6 Quadratic Approximation to &amp.

#955

in Discrete Time

9.7 Quadratic Approximation to &amp

in Continuous Time

9.8 Solving First-Order Conditions by the Galerkin Method

References

List of Mathematical Statements

Solutions to Selected Problems

Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

Z.

Notes:

Includes bibliographical references (p. 208-213) and index.

Description based on publisher supplied metadata and other sources.

ISBN:

9780195356311

0195356314

1-4294-1527-4

1-280-52852-4

0-19-535631-4

0-19-985503-X

OCLC:

935260335