Variaciones del modelo de Hotelling : Modelo de Hotelling: ciudad lineal con funciones de densidad no uniformes. el caso de la función de Kumaraswamy.

Abstract

The present study analyses the Nash Equilibrium for two firms seeking to maximize their profits with respect to their price and location decision, within a market for homogeneous goods in a linear city. It uses Hotelling's two-stage spatial competition model as a basis. Particularly, in this model it is assumed that the distribution of consumers follows a Kumaraswamy function, unlike the original model where this distribution is uniform. It is important to point out that, to determine the analytical solution of the model uses dynamic game theory and the properties of the Kumaraswamy function. On the other hand, in order to contrast the analytical solution, numerical simulations are carried out to determine the Nash Equilibrium. The analytical results obtained suggest that, when the Kumaraswamy function is an increasing or decreasing monotonic linear function, the principle of maximum differentiation between firms is satisfied. On the other hand, the numerical results obtained suggest that initially the principle of maximum differentiation is satisfied, but as consumers conglomerate on one side of the city, there is asymmetry in the equilibrium positions of the firms. That is, one of the firms prefers to maintain its position at the edge of the city and set low prices; while the other firm decides to position itself closer to the conglomeration of consumers and set a higher price, thus leading the market.