Equilibrium Analysis

Rating:
Summary: A superb Introduction to Mathematical Economics!
Review: On little less than 300 pages, Hildenbrand and Kirman give an exceptionally deep introduction to equilibrium analysis. The main topics are Walrasian equilibria (optimal choices relative to a price induced budget set), the core (a generalization of the familiar contract curve), and the relationship between the two. Everything is done in an exchange framework (i.e. no production), which makes it easier to focus on the concepts involved.

Kirman and Hildenbrand prove the existence of Walrasian equilibria, give conditions for the core to be non-empty, show how the core of finite economies converges to the Walrasian equilibria and demonstrate the equivalency between Walrasian equilibria and the core in economies with an continuum of traders. In the last chapter they look at the structure of excess demand functions, conditions for uniqueness and stability in respect to tâtonnement dynamics (no trade until equilibrium is reached). Four appendices give essentially all the mathemtical background needed, except for a little calculus and linear algebra needed in the last chapter. A motivating overview of the content is given in an informal introduction.

All results are well discussed and put in the proper context. The authors don't shy away from showing the limitations of the models. They also point out how one can weaken certain assumptions involved.