book chapter on the maximum principle

Dear Students,

I just uploaded the chapter from my book with Larry Karp on the Maximum Principle. It is merely an alternative to Jon's Note "On Intertemporal Optimization and Dynamic Efficicency" or Michael Hoel's note on the same topic on the reading list. All three readings give you more of a background on the method of dynamic optimization that we are using. 

If you would like to read up using the book chapter then let me summarize that:
- 1-14 covers the maximum principle as used in this class. You can skim over pages 6-8, which give a formal derivation of the maximum principle and instead be satisfied instead with the heuristic provided on page 5. 
- 16-19 introduce you to the closely related Euler equation
- 19-23 introduce the concept of a phase portrait that we will discuss in the renewable resource lectures on fishery. 

In this class we will not cover the more formal analysis starting in section 7.9 and beyond on local dynamics in the neighborhood of the steady state. Of course you are welcome to study it out of mere interest (-:

All the best,
Christian
 

PS: The maximum principle is what we usually refer to as optimal control theory. It is one of two main methods used in economics for dynamic optimization and used the Hamiltonian (or Hamilton canonical equations). The other is termed dynamic programming and uses a so-called Bellman equation. We will at most mention dynamic programming briefly. Resource economics historically builds on the Maximum Principle. Dynamic programming is largely analogous but can have advantageous under uncertainty. Both can be used to derive the Euler equations, which are often an intermediate step in solving the problem and provide economic intuition by themselves.