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Hotelling model

  An analysis of the location strategy of two firms competing for market territory (cf. hinterland). Hotelling was one of the first economists to address the question of the spatial arrangement of competing firms, and his analysis has provided a starting point for a number of illustrative extensions. Hotelling postulated the highly simplified situation of two producers competing to supply identical goods to consumers evenly spread along a linear market. The usual text-book example (though not in Hotelling\'s original presentation) is of two ice-cream sellers competing to supply people evenly distributed on a beach. Under circumstances such as these, Hotelling deduced the seemingly unlikely conclusion that the two sellers would end up standing back-to-back in the centre of the beach, each supplying his own half of the market (see game theory). This was then extended into a generalization concerning industrial agglomeration under certain demand conditions. Hotelling\'s model is thus an illustration of the useful practice of deductive generalization in spatial economic analysis.

Hotelling\'s argument and some of its implications with respect to competition between two firms (duopolists) in space may be illustrated diagrammatically (see figures). Two producers are competing to serve the linear market (a beach) represented by the horizontal axis. Production costs (c) are the same in all locations and the product is sold at a price p reflecting transport cost to the consumer (in the ice-cream case this is the effort of customers walking to the seller\'s location). In figure 1, firm A locates in the centre of the market; B locates some distance to the right. The respective sales areas split at X where the delivered prices from the two suppliers are the same (see market-area analysis). But under the conditions of infinitely inelastic demand when every consumer will buy one unit of the product in one unit of time irrespective of price (or effort of acquisition), firm B loses nothing by moving to the left, as in figure 2, and taking part of A\'s sales area, even though this raises the delivered price to customers on the right. Hence the conclusion that B will join A at the centre of the market, where neither firm can gain further sales by relocating. This conclusion holds irrespective of the initial location of the producers, as long as conditions of infinitely inelastic demand exist. The introduction of sensitivity of demand level to price will discourage sales to distant customers and producers seeking to maximize sales will move apart to the so-called \'quartile\' positions, as in figure 3. Thus the general deduction is that elasticity of demand will stimulate industrial dispersal.

Hotelling\'s model has been applied in other competitive situations, as in public choice theory, and a large literature on the \'spatial theory of voting\' developed from Downs\'(1957) adaptation of the model for political science. (DMS)

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Figure 1

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Figure 2

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Figure 3

References Downs, A. (1957) An economic theory of democracy. New York: Harper & Row. Hotelling, H. 1929: Stabilily in competition. Economic Journal 39: 40-57.

Suggested Reading Smith D.M. 1981: Industrial location: an economic geographical analysis, 2nd edn. New York: John Wiley, 91-7.



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