Optimal monopoly market area spanning in multidimensional commodity spaces

A monopoly Arm locates in multidimensional product characteristics' space by setting a price that mtaximizes its profits. The monopoly market area (MMA) it serves strikes the happy medium between lower price and larger MMA, assuming absence of price discrimination, by setting the price at the MMA margins. The MMA takes different shapes, such as hyperspheres or hypercubes, depending on how customers perceive the product distance from their ideal tastes. Commodity space dimensionality, a measure of customer taste elaboration, has a robust effect on optimization: the optimal MMA stretch increases and price decreases with dimensionality, with different customer sensitivity patterns in place.