Chapter

Dynamic Optimization in Discrete Time

GREGORY C. CHOW

in Dynamic Economics

Published in print April 1997 | ISBN: 9780195101928
Published online October 2011 | e-ISBN: 9780199855032 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195101928.003.0002
Dynamic Optimization in Discrete Time

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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

Chapter.  5165 words. 

Subjects: Financial Markets

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