Book contents
- Frontmatter
- Contents
- List of illustrations
- Introduction to the second edition
- Preface to the second edition
- Preface to the first edition
- Table of notation
- Table of assumptions
- A General equilibrium theory: Getting acquainted
- B Mathematics
- C An economy with bounded production technology and supply and demand functions
- D An economy with unbounded production technology and supply and demand functions
- E Welfare economics and the scope of markets
- F Bargaining and equilibrium: The core
- 21 The core of a market economy
- 22 Convergence of the core of a large economy
- G An economy with supply and demand correspondences
- H Standing on the shoulders of giants
- Bibliography
- Index
22 - Convergence of the core of a large economy
from F - Bargaining and equilibrium: The core
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of illustrations
- Introduction to the second edition
- Preface to the second edition
- Preface to the first edition
- Table of notation
- Table of assumptions
- A General equilibrium theory: Getting acquainted
- B Mathematics
- C An economy with bounded production technology and supply and demand functions
- D An economy with unbounded production technology and supply and demand functions
- E Welfare economics and the scope of markets
- F Bargaining and equilibrium: The core
- 21 The core of a market economy
- 22 Convergence of the core of a large economy
- G An economy with supply and demand correspondences
- H Standing on the shoulders of giants
- Bibliography
- Index
Summary
Replication: A large economy
There is a long-standing tradition in economic theory emphasizing the importance of large (“thick”) markets in maintaining competition. The underlying idea is that if the number of agents in the market is large enough, then no single agent can have monopoly power. Consequently, a competitive price-taking equilibrium will be maintained. Our task in this chapter is to present a rigorous statement and proof of this result in the model of the core of a market economy. We will show that, in a large economy, the core allocations are nearly identical to the competitive equilibrium allocation. That is, in a large economy, there is virtually no incremental return to the monopolistic strategic behavior associated with coalition formation (the strategic behavior assumed in the core). Hence, in a large economy, there is no point in behaving strategically. The best an agent can do is to follow price-taking competitive behavior. This result is actually quite general in models where no single trader is large relative to the size of the market. The version of the theorem we will present in sections 22.1 to 22.3 depends on the idealization that the economy becomes large (and hence each trader becomes strategically negligible) through successive replication of the set of traders. The treatment in section 22.4 is more general at the cost of greater mathematical detail.
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- Information
- General Equilibrium TheoryAn Introduction, pp. 256 - 274Publisher: Cambridge University PressPrint publication year: 2011