Spatial competition between shopping centers

We study competition between two shopping centers that sell the same set of goods and are located at the extremes of a linear city, without restricting consumers to make all their purchases at a single place. In the case of competition between a shopping mall (set of independent single-product shops) and a department store (single multiproduct shop), we find that: if the number of goods is low, all consumers shop at a single place; if it is moderately high, some consumers travel to both shopping centers to buy each good where it is cheaper (a single good is cheaper at the shopping mall). The shops at the mall, taken together, obtain a lower profit than the department store. Nevertheless, two shopping malls should be expected to appear endogenously.