Part 2 of 7
Dynamic Programming
Bellman equations, recursive methods, and competitive equilibrium in dynamic settings.
This part of the course develops the mathematical tools and notation used in dynamic programming problems of the type encountered in applications across macroeconomics. necessary to study how random variables affect optimization problems.
We start with an overview of non-stochastic (or deterministic) dynamic programming problems and the main mathematical results that allow us to solve them. The exposition follows almost verbatim Stokey et al. (1989, Ch. 3). The main objective here is just having a reference for the main results in dynamic programming.
Having established the basics we extend the notation and the basic results to be able to deal with stochastic problems. This follows Stokey et al. (1989, Ch. 9). The objective of this section is to mention the main results without getting into details as they are all extensions of the non-stochastic case.
Finally, we will use these tools to tackle centralized and decentralized economies in the context of the Neoclassical Growth Model. We will first layout the decentralized version of the model and define equilibrium. Having done that we can discuss how to solve the model using the centralized problem. Finally we discuss the nature of the solution in terms of Markov chains and their properties.