The problem of the spatial monopolist is well known where, facing a spatial distribution of consumers with the same tastes and resources, the firm seeks to optimize. Shopping behavior is invariably assumed to be deterministic but in this paper a version of stochastic behavior is used instead. Specifically, the density parameter of the Poisson distribution is adopted to represent the expected demand of those spatial households. So consumers found at different locations generate different frequencies of shopping trips to the spatial firm. In turn, these location-specific trip frequencies vary with the firm's optimizing price, which is determined in the usual way. Subsequent aggregation over all possible locations allows for the identification of the trip volume and the market demand for each feasible trip frequency. The paper also assesses how consumer heterogeneity, a feature of all advanced societies, will affect the various solutions. Three groups (poor, average, and rich) of consumers with different demand attributes are considered. The spatial monopolist now sets an optimizing price that weights each group's specific demand parameters. The stochastic distribution of shopping trips necessarily shifts to reflect this modification to spatial demand. Numerical comparative statics indicate how market solutions shift for small changes in marginal cost, household demand, transportation cost, and consumer heterogeneity.

JEL Classification: D11, D21, R22