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CHAPTER 6

Dynamic Programming and Optimal Growth
This chapter will provide a brief introduction to infinite horizon optimization in
discrete time, focusing particularly on stationary dynamic programming problems
under certainty. The main purpose of the chapter is to introduce the reader to
dynamic programming techniques, which will be used in the rest of the book. Since
dynamic programming has become an important tool in many areas of economics
and especially in macroeconomics, a good understanding of these techniques is a
prerequisite not only for economic growth, but also for the study of many diverse
topics in economics.
The material in this chapter is presented in three parts. The first part provides
a number of results necessary for applications of dynamic programming techniques
in infinite-dimensional optimization problems. However, since understanding how
these results are derived is important for a more thorough appreciation of the theory of dynamic programming and its applications, the second part, in particular,
Sections 6.3 and 6.4, will provide additional tools necessary for a deeper understanding of dynamic programming and for the proofs of the main theorems. The
material in these two sections is not necessary for the rest of the course and it is
clearly marked, so that those who only wish to acquire a working knowledge of
dynamic programming techniques can skip them. The third part then provides a
more detailed discussion on how dynamic programming techniques can be used in
applications and also presents a number of results on optimal growth using these
tools.
Throughout this chapter, the focus is on discounted maximization problems
under certainty, similar to the maximization problems introduced in the previous
chapter. Dynamic optimization problems under uncertainty are discussed in Chapter
17.
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