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  • Print publication year: 2011
  • Online publication date: June 2012

22 - Convergence of the core of a large economy

from F - Bargaining and equilibrium: The core

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.