Book contents
- Frontmatter
- Contents
- List of illustrations
- Foreword
- Preface
- Table of notation
- A Getting started
- B An economy with bounded production technology, supply and demand functions
- C An economy with unbounded production technology, supply and demand functions
- D Welfare economics
- E Bargaining and equilibrium: The core
- F The scope of markets
- G An economy with supply and demand correspondences
- H Conclusion
- Bibliography
- Index
B - An economy with bounded production technology, supply and demand functions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of illustrations
- Foreword
- Preface
- Table of notation
- A Getting started
- B An economy with bounded production technology, supply and demand functions
- C An economy with unbounded production technology, supply and demand functions
- D Welfare economics
- E Bargaining and equilibrium: The core
- F The scope of markets
- G An economy with supply and demand correspondences
- H Conclusion
- Bibliography
- Index
Summary
In Chapters 4 – 7 we will develop a version of the complete Arrow-Debreu model of the economy. The theory of the firm and production sector is presented in Chapter 4 and that of households and demand in Chapter 5. We bring them together with the Walras' Law in Chapter 6 and existence of general equilibrium in Chapter 7.
As we noted in Chapter 2, the typical characterization of economic activity of firms and households is as a maximization subject to constraint. Recall the corollary to Theorem 2.7. In order for maximization to be well defined, sufficient conditions are that the maximand be a continuous function of its arguments and that the opportunity set be compact. That pretty well sets the agenda for characterizing firm and household behavior. We have to find continuous functions for them to maximize. We should find compact constraint sets for them to do it on. That will characterize firm supply and household demand behavior. Although these are not necessary conditions, they are the best generally sufficient conditions available.
Finding continuous functions for the firm and household to optimize does not pose a problem. For the firm, the obvious choice is profits. For the household the traditional maximand is utility, though we will go to some effort to derive the continuous utility function from the more primitive assumption of a preference ordering.
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- General Equilibrium TheoryAn Introduction, pp. 71 - 72Publisher: Cambridge University PressPrint publication year: 1997