This paper intends to look into what would happen if we integrate the “fashion-chasing effect” into the Hotelling model. In the model setup, consumers are assumed to be fashion-chasing, i.e., they obtain higher utility by choosing one of the two products that have higher market share. This kind of consumption behavior is very commonplace nowadays, especially in some markets like IT or fashion industries. Also, these markets are featured by oligopoly competition, which is very close to the Hotelling model setting. Thus, embedding of the “fashion-chasing effect” would make Hotelling model a more powerful analyzing tool in this kind of problem.
2. Methods
In this paper we in general take the standard Hotelling model setups. There are two firms, say firm 1 and firm 2, in the market of a certain product. Their products are assumed to be close substitutes, and differentiate from one characteristic, like the depth of color or sweetness. The firms decide their “positions” on a unit axis from [0,1], here the position can be interpreted as the choice of the characteristic mentioned above. The consumers are identical and assumed to be uniformly distributed over a unit line from [0,1], their coordinators represent their “inherent taste” for the good. Each consumer has unit demand for the certain good, they either buy product from firm 1 or firm 2. If the positioning of the product they buy does not overlap with their coordinate, they are going to pay a travelling cost. So far the model setup is no different with the standard Hotelling model, but we will make some changes in the form of utility function. We introduce the assumption that the consumers are “fashion-chasing”, i.e., their utility is to the direct proportion to the market share of the product they purchase. Mathematically, the utility function of buying the product from firm i is listed as below:
Ui=vsi-c|t-xi|-pi, i=1,2
si is the market share of firm i, c is the unit transportation cost, xi is the position of firm i, pi is the price of firm i, v is a constant.
3. Results
The difference in assumptions deviate the result of this model from the standard Hotelling case. In our calculation, the competition turns out to be a “chick” game: if the consumers behave like fashion-chasers, the two firms on the market would have negative profits. In this case, they can either choose “straight” strategy and get a negative profit, or choose “swerve” to leave the market, the firm left in the market would have a positive profit. As a result, the market can only have one survivor left. This is quite like what is happening in some industries with this kind of network externality: two companies raise a lot of venture capitals and operate with a long time of deficit, until one firm successfully drives another away.