Dynamic Economics Optimization by the Lagrange Method

by Chow, Gregory C.

• ISBN13: 9780195101928
• ISBN10: 0195101928
• Format: Hardcover
• Copyright: 1997-02-13
• Publisher: Oxford University Press

Summary

This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The author presents the optimization framework for dynamic economics in order that readers can understand the approach and use it as they see fit. Instead of using dynamic programming, the author chooses instead to use the method of Lagrange multipliers in the analysis of dynamic optimization because it is easier and more efficient than dynamic programming, and allows readers to understand the substance of dynamic economics better. The author treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance and dynamic games. The book also teaches by examples, using concepts to solve simple problems; it then moves to general propositions.

Author Biography

Gregory C. Chow is Class of 1913 Professor of Political Economy, Professor of Econometrics, and Director of the Econometric Research Program at Princeton University. He has also advised the Prime Ministers of Taiwan and China on economic policy and reform. He is the author of numerous books, including Analysis and Control of Dynamic Economic Systems (1975), Econometrics (1983), and Understanding China's Economy (1994).

Table of Contents

Chapter One Introduction	3	(16)
1.1 Dynamic Economics and Optimization	3	(4)
1.2 Methods of Dynamic Optimization	7	(3)
1.3 Economic Growth	10	(2)
1.4 Theories of Market Equilibrium	12	(1)
1.5 Business Cycles	13	(1)
1.6 Dynamic Games	14	(1)
1.7 Models in Finance	15	(1)
1.8 Models of Investment	16	(1)
1.9 Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems	17	(2)
Chapter Two Dynamic Optimization in Discrete Time	19	(13)
2.1 The Method of Lagrange Multipliers by an Example	19	(1)
2.2 The Method of Dynamic Programming by an Example	20	(2)
2.3 Solution of a Standard Dynamic Optimization Problem	22	(1)
2.4 Numerical Solution by Linear Approximations of h and g	23	(2)
2.5 Sufficient Conditions for a Globally Optimal Solution	25	(3)
2.6 Relations to Known Results on Optimization	28	(2)
Problems	30	(2)
Chapter Three Economic Growth	32	(19)
3.1 The Brock-Mirman Growth Model	32	(2)
3.2 A Multisector Growth Model	34	(3)
3.3 A Growth Model Based on Human Capital and Fertility	37	(5)
3.4 Technology and Economic Growth	42	(5)
3.5 Research and Development and Economic Growth	47	(2)
Problems	49	(2)
Chapter Four Theories of Market Equilibrium	51	(29)
4.1 Asset Prices of an Exchange Economy	51	(2)
4.2 Equilibrium in a Pure Currency Economy	53	(2)
4.3 A Pure Credit Economy with Linear Utility	55	(2)
4.4 Money and Interest in a Cash-In-Advance Economy	57	(9)
4.5 A One-Sector Model of General Equilibrium	66	(5)
4.6 Equilibrium of a Multisector Model	71	(5)
4.7 Equilibrium of a One-Sector Model with Tax Distortion	76	(2)
Problems	78	(2)
Chapter Five Business Cycles	80	(31)
5.1 Keynes and the Classics	80	(1)
5.2 Dynamic Properties of a Multisector Model with Technology Shocks	81	(2)
5.3 Estimating Economic Effects of Political Events in China	83	(2)
5.4 Estimating and Testing a Base-Line Real Business Cycle Model	85	(8)
5.5 Real Business Cycles and Labor Market Fluctuations	93	(7)
5.6 Oligopolistic Pricing and Aggregate Demand	100	(7)
5.7 Research on Real Business Cycles	107	(2)
Problems	109	(2)
Chapter Six Dynamic Games	111	(28)
6.1 A Formulation of Models of Dynamic Games	111	(1)
6.2 Price Determination of Duopolists with No Consumer Switching	112	(4)
6.3 A Characterization of Subgame Perfect Equilibrium for Infinitely Repeated Games	116	(3)
6.4 A Characterization of Subgame Perfect Equilibrium for Dynamic Games	119	(4)
6.5 Credible Government Policy	123	(8)
6.6 Credible Taxation to Redistribute Income	131	(6)
Problems	137	(2)
Chapter Seven Models in Finance	139	(33)
7.1 Stochastic Differential Equations	139	(2)
7.2 Dynamic Programming for a Continuous-Time Model	141	(1)
7.3 Solution of a Continuous-Time Optimization Problem by Lagrange Multipliers	142	(3)
7.4 An Algebraic Method for Finding the Optimal Control Function	145	(2)
7.5 Optimum Consumption and Portfolio Selection Over Time	147	(5)
7.6 Capital Asset Pricing with Shifts in Investment Opportunities	152	(2)
7.7 The Pricing of Options and Corporate Liabilities	154	(2)
7.8 Asset Pricing and Portfolio Selection with Noise in Supply	156	(6)
7.9 Asset Pricing and Portfolio Selection with Asymmetric Information	162	(1)
7.9a The Kalman Filter in Continuous Time	162	(5)
Problems	167	(5)
Chapter Eight Models of Investment	172	(13)
8.1 Investment as Exercising an Irreversible Option to Invest	172	(2)
8.2 A Simple Model of Investment with Adjustment Cost	174	(2)
8.3 Investment as Gradual Capacity Expansion with Adjustment Cost	176	(3)
8.4 Optimal Policy for Replacement Investment	179	(2)
8.5 Optimal Policy to Retire Human Capital	181	(1)
8.6 Some Other Literature on Investment	182	(1)
Problems	183	(2)
Chapter Nine Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems	185	(23)
9.1 Introduction	185	(1)
9.2 Change of Variables	186	(4)
9.3 A Short-Cut to Log-Linearize First-Order Conditions	190	(2)
9.4 Solving Matrix Riccati Equations Rapidly	192	(3)
9.5 Solving Linear First-Order Conditions by the Method of Undetermined Coefficients	195	(2)
9.6 Quadratic Approximation to h in Discrete Time	197	(3)
9.7 Quadratic Approximation to h in Continuous Time	200	(2)
9.8 Solving First-Order Conditions by the Galerkin Method	202	(5)
References	208	(6)
List of Mathematical Statements	214	(2)
Solutions to Selected Problems	216	(12)
Index	228