Two papers that delve into the economic theory behind the positioning of markets and firms.
There are certain regions in every city that are known commonly for providing a specific type of good or service. For instance, the Muhammad Ali Road in Mumbai is famous as a khau galli (food street) for a variety of delicacies it offers. Similarly in Bangalore, places like Infantry Road and Thippasandra Market are known for a wide range of furniture shops located within a small radius.
The economic theory that explains this clustering of homogenous firms was originally developed by, a US economist, Harlod Hotelling in an article titled “Stability in Competition” in 1929.
Hotelling’s Competitive Location Theory
Case 1 ——A————-———————B——
Case 2 ————————A-B———————
Fig: Depicting the location of Firms A and B before and after the Hotelling’s law is applied
Hotelling’s theory states that the competitors tend to locate their firms arbitrarily close to each other. As per the theory, firms located at A and B in the Case 1 would be able to attract a larger customer base if they move towards the centre. For instance, if firm A shifts to the right it would draw a more customers as the population in the middle which was previously indifferent between the two firms would now prefer A.
This theory is based on the assumption that the firms use the free on board pricing method, whereby, the customers pay for the transportation. Therefore, the consumers would prefer the nearest option in order to reduce the cost incurred. The example provided in the paper is of fast food franchises.
Take the example of food stalls. Here, food can be considered as a homogenous good. These food stalls price their dishes based on the production cost (cooking and raw material). Since the customers have to pay to reach the location, they prefer the food stall nearer to home. Hence, if there were two food-stalls serving similar dishes at the two ends of a city, their customer base would be limited to the region closer to their end. However, by shifting towards the centre both the food stalls would also be able to attract the customers that stay in between the two ends. Hence both of them would continue to shift to the centre until they are both clustered in the middle. It is this region with the clustered food shops that creates the well-known food streets like Mohammad Ali Road in Mumbai and Paratha galli in Delhi. This is known as the Hotelling’s law or the principle of minimum differentiation.
‘Inherent Instability’ in the Location theory
In 1996, HA Eiselt and Gilbert Laporte wrote a paper titled “Equilibrium results in Competitive location models” essentially studying Harold Hotelling’s Competitive location theory and its applications.
Eiselt and Laporte’s paper makes the case that competitive location theory is “inherently unstable”. The primary reason given is the interplay of forces exerted on the firms due to the pull and push factors. Pull factor is the additional market share that the location offers, whereas, the high price competition amongst the competitors acts as a push factor by restricting the firm’s revenue. The authors claim that the optimal location for an individual firm would be decided based on a trade off between the new area gained and the old area lost, provided all other facilities remain at their present location.
“At some critical distance, a different facility may be closer to that point and hence customers will switch to the closer facility. This is the same feature that occurred in a linear market with more than two facilities, but it was not present in case of only two facilities. Consequently, the possible loss of customers to competitors is due to the number of competing facilities, and not to the differences in the dimensionality of the given space.”
The paper goes on to explain that the location model would continue to be unstable until Nash equilibrium is attained. Nash equilibrium refers to the situation where each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy. In the case of firm location, if the firms choose both price and location, the Nash equilibrium would be reached when both the firms enjoy equal profit. As mentioned in the paper, in cases where the customers are randomly distributed, facilities would cluster around the median of the market rather than the midpoint of the market.
The authors conclude that the way forward would be to explore the modelling of customer behaviour and to use networks rather than one-or two-dimensional spaces for modelling.
Other application of the Competitive location theory
Eiselt and Laporte’s paper also provides non-standard examples like one of print films. They trace the feature space of the film by assigning a dimension to each feature of the film such as speed, grain, tolerance of extreme temperatures, colour rendition etc. Following which the various brands selling print films are mapped based on the features they offer. The potential customers are asked to choose any two features they prefer which are then marked within the space. Using the competitive theory in this case, the customers are expected to purchase the product closest to their “ideal product”.
In this way, “It’s now possible to construct market areas for each of the products in a way so that the market area of a product includes all customers which are closer to his market area than that of any of the other products.”
Another interesting application of location model provided was on electoral politics, which has been further studied by Anthony Downs in his paper titled “An Economic Theory of Political Action in a Democracy” (1957). As per Eiselt and Laporte’s paper,
“In political models, the objective is to position political candidates in an issue space, very similar to the feature space introduced above, except that its axes do not represent features of a class of products, but issues deemed important by the electorate. Assuming again that the issues are measurable on a quantitative scale, each political candidate and each voter could be represented in that space. Clearly, prices do not exist in this model. One possible objective could now be for each candidate to position himself so as to maximise his number of voles.”
However, the paper itself explains the problems with model as- first, many issues cannot be measured quantitatively, second, all the voters cannot practically be mapped into the space defined and third, locating candidates according to the vote maximising location would place the candidates at far removed locations from some of their supporters.
Photo: Meena Kadri
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