Modeling the Stackelberg strategy in a linear model (linear city) Hotteling

Abstract

The article examines the model of a linear city with exogenous Stackelberg competition between two firms. In
this model, at low transport costs, firms in equilibrium are located at one point in the center of the market, while the profit of
the leader firm is twice the profit of the follower firm, the price is minimal, and the quantity of products supplied is maximal
at the point where the firms are located. At higher transport costs, firms differentiate, and the market, as it were, splits into
two “submarkets”: the leader firm sells the bulk of production near its location, and the follower company sells the bulk of
its products, while the profit of the leader firm exceeds the profit of the follower firm by less than twice, the price is always
minimal at the point of location of the leading firm. With an increase in transport costs, the quantities of products supplied
by firms decrease, and the price rises.