Market share, distance and potential

Abstract

Suppose that in every location the ratio of sales by two firms offering heterogeneous products depends only on the difference of economic distance from the two plants, suitably defined. Then the market share is a simple function of distances. Market areas, defined as those subregions where market share of some firm dominates that of any other firm, are identical with conventional market areas for sellers of an homogeneous product. Next curves of equal market share — isoshare lines — are introduced, discussed and calculated for special cases. It is shown that under certain restrictions on the function which specifies the distance effect and on the measure of economic distance, the present approach is consistent with demand analysis based on utility functions. Finally, the hypothesis is related to the gravity and potential concepts that have been used in travel forecasting and in other contexts of regional science. In a market with heterogeneous products how is market penetration affected by distance? How does the competitive position of supermarkets, newspapers, shopping centers, recreational facilities, schools, cultural centers, service centers, cities, tourist attractions, national parks and foriegn countries depend on distance? Questions like these cannot be answered by a non-critical application of conventional models of market and supply areas as developed in location theory, since these are based on the assumption of homogeneous goods. One possible way of coping with the effect of distance which is suggested by general social science — or sometimes “social physics” — is to introduce a concept of attraction decreasing with distance along the lines of Newtonian field theory. However, the underlying economic reasoning is often vague and obscure. The purpose of this paper is to state a simple hypothesis concerning the effect of distance on demand and to demonstrate its implications. This will incidentally produce an extension of the range of application for conventional market and supply areas and will serve to give operational meaning to the gravity or potential theory of spatial competition.