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Lecture Notes on Dynamic Programming

Lecture Notes on Dynamic ProgrammingEconomics 200E, Professor Bergin, Spring 1998 Adapted from Lecture Notes of Kevin Salyer and from Stokey, Lucas and Prescott (1989)Outline1) A Typical Problem2) A Deterministic Finite Horizon ) Finding necessary ) A special ) Recursive solution3) A Deterministic Infinite Horizon ) Recursive ) Envelope ) A special ) An analytical ) Solution by ) Solution by iteration4) A Stochastic ) Introducing ) Our special case ) Finding Typical ProblemConsider the problem of optimal growth (Cass-Koopmans Model). Recall that in the Solowmodel the saving rate is imposed, and there is no representation of preferences. The optimalgrowth model adds preferences for households, and derives an optimal saving rate. Utilityis maximized for the representative agent, given the technology that they re faced with. Thesocial planner s problem may be described as are summarized in the utility function:LES| c|'fc c4 Utility is assumed to be time-separable, that is, marginal utility of consumption today dependson today s consumption only.

Lecture Notes on Dynamic Programming Economics 200E, Professor Bergin, Spring 1998 ... Consider the problem of optimal growth (Cass-Koopmans Model). Recall that in the Solow ... it too would be a control variable. The first order condition for the equation above is:

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  Programming, Control, Dynamics, Optimal, Dynamic programming

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