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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\rho \in (0,1)$</EquationSource> </InlineEquation> 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 <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation> is small, increasing <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation> increases optimal specialization. However, when <InlineEquation ID="Equ4"> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation> is close to 1, increasing <InlineEquation ID="Equ5"> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation> further has no effect on the optimal allocation. I also show that optimal specialization is gradual over time when there is cost to reduce specialization. Even for small <InlineEquation ID="Equ6"> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation>, the process converges to the unconstrained optimum that would occur under <InlineEquation ID="Equ7"> <EquationSource Format="TEX">$\rho=1$</EquationSource> </InlineEquation>. Copyright Springer-Verlag Berlin/Heidelberg 2005