The extent of the market and optimal specialization

In this paper I examine how the socially optimal allocation, and specialization in particular, depends on the extent of the market. I interpret the society's ability to keep transaction records as the extent of the market and measure it by a probability ρ ∈ (0,1) with which the society can update agents' past transactions into the public record. The society uses this record to detect potential defections from the optimal allocation and to punish the defectors with autarky. I show that when ρ is small, increasing ρ increases optimal specialization. However, when ρ is close to 1, increasing ρ further has no effect on the optimal allocation. I also show that optimal specialization is gradual over time when there is cost to reduce specialization. Even for small ρ, the process converges to the unconstrained optimum that would occur under ρ = 1.