Computation
All of the results presented here have been about existence of solutions and characterization of the form of the value functions, solutions and the properties of the policy functions or optimal plans.
Dynamic programming techniques are also widely used in explicit (numerical) computations (Exercise 6.3 below provides one useful starting point in this respect). In particular, the recursive formulation of dynamic programming problems also presents an effective computational approach. This is particularly useful, since as hinted at by the discussion in Example 6.4, only certain very special dynamic optimization problems yield closed-form solutions. Therefore, economists, like engineers, must often use computational tools in order to obtain various qualitative and quantitative insights about solutions to optimization and equilibrium, and dynamic programming is the main starting point of these approaches.Space restrictions preclude me from providing a discussion of various computational tools and how dynamic programming methods are used in numerical analysis. This should not be interpreted as downplaying the importance of computation in the study of economic growth and the usefulness of dynamic programming approaches in computation. The reader is encouraged to consult Judd (1998) for an excellent and thorough discussion of computational issues in economics and the role of dynamic programming. Ljungqvist and Sargent (2005) also provide a brief introduction to use of computational methods in macroeconomics.
6.11.