In this paper, we re-examine Mendelson’s model for the equilibrium price of a double-blind Dutch auction with Poisson-distributed stochastic demand and supply. We present a number of new results. We focus on the various ways that demand and supply cross. We identify four different categories of crossing, extending Mendelson’s results which are based on a single category of crossing. Secondly, conditioning on quantity, we derive the joint distribution of the relevant demand and supply prices associated with such two-sided markets originally described by Bohm-Bawerk (1891). The distributional result is extended to the case where the limit orders on different sides of the market arrive at different rates. Finally, we derive the distributional properties of the price elasticities.