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

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

Chapter:
(p.185) Chapter Nine Numerical Methods for Solving First-Order Conditions in Dynamic Optimization Problems
Source:
Dynamic Economics
Author(s):

GREGORY C. CHOW

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195101928.003.0009

While there have already been a large number of efforts to explain the numerical solutions to dynamic optimization problems that are based mainly on dynamic programming, in this chapter the author attempts to veer away from using the value function and the Bellman equation that can be derived from the former, and to draw more attention to the first-order conditions for determining the optimum allocations based on the method of Lagrange multipliers. The author asserts that utilizing the Lagrange method is one of the most efficient procedures in several different applications since, with the exception of the Lagrange function, resources are wasted so that information regarding the value function may be acquired and stored. The author illustrates numerical methods in finding the solutions to first-order conditions in both continuous time and discrete time.

Keywords:   continuous time, discrete time, first-order condition, value function, numerical methods

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