Section 1 Study Problems: September 19

Problem

Important general concepts

Problem 1: Dynamic programming and a neoclassical model of capital formation

 

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Dynamic programming is a recursive (iterative)  procedure in which a value and policy function is constructed at each step. The problem studies a simple example in which both can be constructed in closed form. It is also possible to determine that the limit of a series of iterations is the same (value, policy) function that would be determined directly from the infinite horizon value function.

Problem 2: Dynamic programming and labor market search

 

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Dynamic programming can be applied to decision problems in which the choice (control) set is discrete, rather than continuous

 

State evolution and controls are then a discrete Markov process (Markov chain)

Problem 3: Dynamic programming and particular non-time separable preferences

 

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If the departures from time separability in and objective can be cast in a recursive form, then dynamic programming can be applied.

 

For smooth dynamic programs, the FOCs and ETs can be calculated, even if an analytical solution can be found