Academic journal article Economic Inquiry

Product Differentiation under Congestion: Hotelling Was Right

Academic journal article Economic Inquiry

Product Differentiation under Congestion: Hotelling Was Right

Article excerpt


Nobody goes there anymore; it's too crowded. --attributed to Yogi Berra

In the seminal Hotelling (1929) model of spatial competition, two firms compete to sell a product. In Stage 1, they locate along a unit line; in Stage 2, they set their prices. Consumers spread evenly along the line choose the best deal based on the posted price and linear transportation costs.

Hotelling apparently solved for the Stage 2 equilibrium in pure strategy prices, and via backward induction showed that regardless of location, either firm would increase its profits by moving closer to its competitor. (See Figure 1, first line.) This gave rise to the "principle of minimum differentiation"--the tendency of competing firms to make similar choices in geographical or product-characteristic dimensions.

D'Aspremont, Gabszewicz, and Thisse (1979) critiqued this principle's validity within the Hotelling model. They showed that no pure strategy pricing equilibrium exists when the firms are sufficiently close together (but not at the same location). This is because for firms at close quarters, the temptation is strong for one firm to cut its price just enough to steal the entire mass of customers located on the other side of its competitor. In fact, if locations are symmetric, the Hotelling pricing equilibrium exists only if firms locate in the outer quartiles. Thus, Hotelling's backward induction breaks down and there is no guarantee that firms located in the inner quartiles would want to move closer to each other. (See Figure 1, second line.)

At this point the literature diverges. Much of the literature follows d'Aspremont, Gabszewicz, and Thisse (1979), who introduce quadratic transportation costs and show that they provide greater tractability. (1) With quadratic costs, the differentiation result is reversed: firms maximally differentiate in equilibrium. (2)

Osborne and Pitchik (1987) continue with Hotelling's linear transportation costs, despite the tractability challenges. They characterize a mixed strategy pricing equilibrium when firms are located close to each other. In the symmetric subgame perfect equilibrium with pure location choices that they compute, both firms locate at the edges of the inner quartiles, 0.24 of the distance from the midpoint. (See Figure 1, third line.) Thus, substantial (near-efficient) differentiation remains in equilibrium. Evidently, firms' incentives are to move farther apart over much of the region where Hotelling's pricing equilibrium fails to exist.

This paper also retains linear transportation costs, and adds one feature to the model--negative network externalities. Specifically, consumers are assumed to derive disutility in proportion to the number of customers of the firm they patronize. This negative externality can be interpreted as congestion arising from firm capacity constraints--queuing for parking, customer service, or to pay. (3) In many cases, the more crowded a store or restaurant, the less attractive it is to patronize, all else equal. It can also be interpreted as a specific kind of snobbery which we term "brand snobbery": preferring the brand less consumed. (4)

We find that the greater are congestion costs relative to transportation costs, the more of Hotelling's line contains a Hotelling-like pure strategy pricing equilibrium. The centered interval where the equilibrium does not exist for symmetrically located firms shrinks as congestion costs grow in importance, and in the limit vanishes. That is, the Hotelling pricing equilibrium can be supported at any location where the firms are located on opposite sides of the midpoint, given sufficiently high congestion costs relative to transportation costs.

This result has implications for product differentiation. In essence, congestion costs extend the portion of the line over which Hotelling logic applies, that is over which firms can increase profits by moving closer to each other. …

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