About Competition Between Firms: Equilibrium or Disruption?

One resumes the notion of “monopolistic competition” or product differentiation. The model used is Bertrand competition, the demands being deduced from the consumers’ utilities. A consumer is represented by a point ui in the cube 0 ≤ ui ≤ 1, ui being the utility of the product i for him. The product differentiation is when the points representing the consumers are in the facets of the cube ui = 1. One studies the mathematical properties of the equilibrium. Some of them correspond to the characteristics of product differentiation, which are: (1) all the consumers make a purchase. When the products are differentiated, the firms are innovative (since the preferred product of a consumer has a utility which is maximal). And innovation has been defined “struggle against no consumption” (Christensen) (2) each firm has its “garden”, consumers in the facet ui = 1 for the firm Ei. A firm keeps the consumers in its “garden”, provided its price is not too high (3) given the existence of “gardens” the profits are sufficient. Product differentiation is symmetrical, and disruption is dissymmetrical: the disruptive firm has a “garden” with a utility higher than the utilities of the “gardens” of its competitors. One demonstrates that the profit of a disruptive firm increases. The goals of the paper are: - To set out a model which describes product differentiation and disruption; - To explore the possibilities of the model used (Bertrand competition, the demands being deduced from the consumers’ utilities). The author has already used this model to study a particular kind of merger: when the merger is profitable, the bought asset being closed down. It is a sign of saturated market. Even, it could be a criterium (for saturated markets) interesting for fintechs. Also, the model allows discriminating non differentiating innovation (when there is product differentiation and all the utilities increase) and differentiating innovation (disruption: only the utility of the product of the disruptive firm increases). One shows that differentiating innovation provides more profit, always, but non differentiating innovation could provide no more profit. Finally, the model is also useful to study the effects of cannibalization. In the paper, a tractable example is set out, allowing to answer this question: is it in the interest of a disruptive firm to buy and close down a competitor before disruption? If the competitor cannibalizes the product of the disruptive firm very much, it is better to buy and close down this competitor.