The Extent of the Market and the Optimal Degree of Specialization

In this paper I examine the socially optimal allocation in a random matching economy. The optimal allocation is supported by punishment to defections, using the public record of agents<92> transaction. However, public record-keeping is imperfect, as an agent<92>s transaction is updated into the public record with probability r < 1. I interpret r as the extent of the market. When r is small, an extension of the market increases the optimal degree of specialization and the quantities of goods exchanged in the market. When r is large, however, a further extension of the market has no effect on the socially optimal degree of specialization or the quantities of trade. I also examine the optimal allocation when there is an adjustment cost for reducing specialization. In this case, the optimal process of specialization is gradual, even though there is no adjustment cost for increasing specialization.