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Dynamic EconomicsOptimization by the Lagrange Method$
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Gregory C. Chow

Print publication date: 1997

Print ISBN-13: 9780195101928

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195101928.001.0001

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Dynamic Optimization in Discrete Time

Dynamic Optimization in Discrete Time

Chapter:
(p.19) Chapter Two Dynamic Optimization in Discrete Time
Source:
Dynamic Economics
Author(s):

GREGORY C. CHOW

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195101928.003.0002

In dynamic economics, a set of equations are used to describe how state variables undergo dynamic evolution. This set of equations is used in maximizing a specific objective function that proves to be time separable. This chapter includes a sample problem and identifies the functions of the various variables and the elements that they denote. Such solutions of such equations may be obtained through employing the method of Lagrange multipliers, which is also demonstrated in this chapter. Also, the Bellman equation is introduced, and the origins of the concepts of “dynamic programming” and the “principle of optimality” are discussed. In this chapter, we are able to identify the necessary and sufficient conditions that have to be satisfied by the optimal control function and the Lagrange function related to that equation.

Keywords:   objective function, Lagrange multipliers, Lagrange function, dynamic programming, optimality

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