Effects of a customer gradient in a spatial monopoly

Traditional location theory analyzes the behavior of a monopolist selling a good (service) in a spatial market having identical customers distributed at uniform density. However, customers in highly urbanized societies rarely exhibit uniform (flat) densities. Consequently, location theory has lost some of its relevance for clarifying how firms should behave in densely populated spatial markets. This paper uses a downward-sloping function, centered on the point of sales, to represent the type of customer gradient that is now common in urban settings. Therefore, the location-specific demand density for a low-order retail good is determined by the interaction between a (single-good) linear pricing system and a linear customer gradient. The spatial monopolist must adjust its price to both exogenous factors when seeking to maximize profit in the market. Under a mill (f.o.b.) price system, a steeper customer density induces the monopolist to raise its price higher to maintain its profit.