While these two studies are considered significant, they have not escaped criticism. For example, Greenwald and Glasspiegel's argument is not robust regarding the existence of transaction costs; and the existence of the Alchian-Allen effect requires that the seller wield a monopoly in a distant market. In addition, the application of the Alchian-Allen Theorem to slave prices has been criticized by Komlos and Alecke (1996, JIH) -- replied by Pritchett (1997, JIH).
In order to establish a solid foundation for our analysis, we provide an independent estimate of slave prices and develop our own theoretical model. The estimation of slave prices is based on the standard pricing schedule of slaves from Orleans Parish sold by traders from Orleans Parish. From these estimations of the standard pricing schedule for male and for female slaves, we can obtain the price differentials of each slave by place of origin and by year. Using these estimates, we calculate the evolution of price differentials and thereby establish our model. That is, we find an upward-sloping trend in the price differentials and reach an unexpected conclusion about them: that the price of slaves shipped to the New Orleans market from the Old South was not, in fact, higher than that of local slaves, especially before 1830.
Discounting the possibility of influence on the part of state or local legislatures, we treat the evolution of price differentials by means of an adverse selection model: the slave sellers provide a price menu arranged according to the slave types demanded by the slave buyers, and the buyers refer to this menu in bidding for the slaves. In the model, the price menu is designed to encourage the buyers to reveal their preferences (truth telling).
Because certain elements of the general model are difficult to establish, we make use of numerical simulations in order to explain the evolution of price differentials -- in particular, the key variable is not only in the integral intervals but also in the integrand. Reconciling the theoretical model with the empirical findings, we conclude that the net profit of the seller varied in inverse proportion to the productivity of the slaves whom he sold. At first glance, this conclusion seems implausible; however, the role of informational rents in the adverse selection model provides basis of such a net profit function, which receives further support from various interpretations of cliometrical observations.