Spatial differentiation, divisible consumption and the pro-competitive effect of income

We analyze a spatial differentiation model with divisible consumption under one-stop shopping. Each consumer who visits only one store, chooses the quantities of the goods which maximize his/her utility function under the budget constraint (namely consumption expenditures must equal income minus transportation costs), choosing the store which provides him/her with the largest indirect utility. We derive the equilibrium price when the firms are located at the two extremities of Hotelling's linear city and show that income increases have a pro-competitive effect. Equilibrium prices are indeed decreasing with consumers' income and increasing with the transportation cost. They converge to marginal costs as income goes to infinity or the transportation cost goes to zero. However the analysis does not amount to a story of weight of transportation cost relative to income. Equilibrium profits do not change in the same way as the transportation cost decreases or the income increases. They do not tend toward the same limit as the income tends to infinity or the transportation cost tends to zero. Finally the one-stop shopping assumption is discussed. It is mainly proved that it may emerge endogenously.