In 1931, William J. Reilly drew on the law of gravity to create an application of the gravity model to measure retail trade between two cities. His work and theory, The Law of Retail Gravity, allows us to draw the boundaries of commercial areas around cities using the distance between cities and the population of each city. In addition to Newton`s law of gravity in the physical sciences, there were other precursors to Reilly`s “law” of detail gravity. In particular, E.C. Young described a migration formula based on the physical law of gravity in 1924, and H.C. Carey had included a description of people`s tendency to “contract” in an 1858 summary of social science theory. [2] William J. Reilly`s Retail Gravity Act states that customer groups are attracted to certain retail locations based on factors such as distance to market, distance between markets, market population, size of retail facility, location of competitors, etc.
For example, it is assumed that the greater the distance, the less likely shoppers are to travel, but are willing to travel longer distances to large shopping malls. Reilly`s law of retail gravity is a heuristic developed by William J. Reilly in 1931. [1] Under Reilly`s “law,” customers are willing to travel longer distances to large malls because they are more attractive to customers. In Reilly`s formulation, the appeal of the mall becomes an analogy of size (mass) in the physical law of gravity. Reilly`s Law of Gravity in Retail (1931) aims to find a point of indifference between two locations so that the commercial area of each can be determined. This point is considered a function of the distance between two places, considered by their respective sizes (population is often used for this purpose). One location can therefore be more attractive than the other. The law assumes that the geography of the region is flat, without rivers, roads or mountains, to change a consumer`s decision about where to travel to buy goods. It is also assumed that consumers are otherwise indifferent between real cities.
By analogy with Newton`s law of gravity, the point of indifference is the point at which the “attractiveness” of the two shopping centers (postulated as proportional to their size and inversely proportional to the square of the distance between them) is equal: Of course, Reilly`s law assumes that cities are on a flat plain without rivers. Highways, political boundaries, consumer preferences or mountains to change an individual`s progress towards a city. In the figure above, two sites are 75 km apart. According to Hotelling`s principle, the point of indifference should be halfway between (37.5 km). However, since Site A has a larger population (more weight), it is expected to attract more customers. In these circumstances, the point of indifference is 45.9 km from Site A. Reilly`s law has many variations, and the extensions and applications are numerous. These include: The formula is used between two cities to find the BP between the two. The distance between the two cities is divided by one plus the result of dividing the population of city B by the population of city A. The resulting BP is the distance between city A and the 50% boundary of the commercial area.
Reilly realized that the larger a city was, the larger it would have a commercial area, and so it would draw from a larger hinterland around the city. Two cities of equal size have a commercial area border halfway between the two cities. When cities are unevenly large, the border is closer to the smaller town, giving the big city a larger commercial area. where d A {displaystyle d_{A}} is the distance from the point of indifference of A, d B {displaystyle d_{B}} is the distance from B and P A / P B {displaystyle P_{A}/P_{B}} is the relative size of the two midpoints. If the customer is on the line connecting A and B, then if D is the distance between the centers, the point of indifference, measured by A on the line, One can determine the complete commercial area of a city by determining the BP between several cities or centers. As expected, for centers of the same size, d=D/2, and if A is greater than B, the point of indifference is closer to B. Since the size of A becomes very large relative to B, d tends towards D, which means that the client always prefers the largest center unless it is very close to the smallest. Reilly called the boundary between two trading territories the breaking point (BP). On this line, exactly half the population shops in one of the two cities.