Spatial Demand Models with Uniform Rate of Growth

This paper examines the changes over time in the spatial dispersion of facilities in a bounded one-dimensional habitat. Each facility produces a single good for a unique market area and demand for the good varies inversely with distance to the nearest facility and increases uniformly over time. Production and transportation cost functions are not assumed to be linear, and it is assumed that market areas are chosen so as to minimise the average cost of producing and transporting unit amount of the good. Conditions relating the demand function to the transportation cost function are given which are necessary and/or sufficient for the size of the market area to decrease over time. It is shown that if the market area has constant size, ‘balanced growth’ occurs if and only if the demand function is of the Pareto type. Finally, the relevance to this analysis of economies of scale is discussed.