Ebook Horizontal differentiation and price competition with sequential entry
In its pioneering paper ’Stability in competition’, Hotelling (1929) modelled competition among firms with differentiated products. He departed from Cournot’s and Bertrand’s views of perfect substitutes, which implies pure quantity or pure price competition. Hotelling deals with a linear market (Main Street) and considers that all consumers, living along the street, buy one unit of good, choosing the one whose perceived price (mill price plus transportation costs) is smaller.
The two firms compete in price, having different locations, or different characteristics in the product space. His main motivation was to show that competition has not always a ”winner-takes-all” (namely, the leader in price) form, but that small changes in price only affects smoothly the quantity sold by a competitor. In equilibrium, when a firm lowers its price, it does not get the other’s full market share, but only a fringe of them, varying continuously in price change. From this setting, another conclusion has be drawn by Hotelling: if firms choose first their locations, their will be a tendency towards homogeneity of the product: the firms will tend to choose almost the same location, at the center of the market. This is the so-called principle of minimum differenciation.
It is somehow paradoxical that the idea of ’stability’ in competition put forth by Hotelling is actually invalid in his model, on account of indeterminacy of a stable configuration. Indeed, as pointed out by d’Aspremont & al. (1979), an equilibrium does not exist for all possible locations of the firms. If they are too close, a competitive price equilibrium is impossible. Thus the enunciated Principle of Minimum Differentiation does not hold even in Hotelling’s model, because of a non-existence problem. d’Aspremont & al. continue the discussion with an adaptation of the standard model, changing the linear transportation costs into quadratic ones.
As pointed out by MacLeod (1985) this implies that the mass of indifferent consumers is zero, because indifferent consumers are located at a single point. This restores equilibrium existence, as continuity of payoffs is restored. Moreover, in this setting, the reverse result holds about differentiation: the firms locate at the extreme points of the market. Many authors have subsequently found mitigated results about differentiation in equilibrium (Economides 1984, Hinloopen & van Marrewijk 1999 among others).
While differentiation models concern a huge literature, we focus in this paper on the sequentiality of location and price choices. Following Prescott and Visscher (1977), we use subgame perfection as equilibrium concept. In most of the papers, it is assumed that firms choose location first (possibly sequentially) and once for all, then compete simultaneously in price. Lambertini (2002), for instance, studies sequential entry with discounting. In his setting, a leader chooses first a location for the whole game. He is first alone on the market and is thus free to set a monopoly price.
After a certain while, a followers enters the market: he chooses a location and competes in price with the leader. This is consistent with the view that the location is a geographical parameter, or with the view that the design of a product is generically far less flexible than its price. It seems to fit relatively well products that have a long lifetime. Up to our knowledge, the only paper that modifies the assumption of simultaneous pice competition is Anderson (1987). He studies a price leadership configuration: the firms choose sequentially the locations, then a Stackelberg competition in price takes place. The subject of the paper is to determine which firm chooses to be the price leader; the answer is that the second entrant prefers to be price leader, and the first to be price follower. This is such the sequential setting that seems to be the most likely to appear.
One has now to remark that all these standard settings assume that price competition, whatever the form it takes, happens only after both location are fixed. However, situations exist where protagonists in a market commit to a price for a period as long as the product lifetime. Some firms, like chainstores, publish a catalogue (a product-price couple) and stick to it for a while. It could be, for example, that agency situations imply this inertia: an employee that work as a seller is not allowed to lower the price of the product it sells, he is forced to apply the announced price. Situations like these do not fit the classical assumption that price competition occurs last, after everyone has observed which products are in the market. It seems rather that some firms commit to a price, while others react to these leader firms. This is precisely the heart of the analysis we conduct here. In the present model, we study the case where one firm enters first the market and, in addition to the location of its product, commits to its price. Then a second firm chooses its location and price, knowing the other’s catalogue. This is a Stackelberg setting for the couple of variables (location, price).
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