# Reilly's law of retail gravitation

In economics, Reilly's law of retail gravitation states that larger cities will have larger spheres of influence than smaller ones, meaning people travel farther to reach a larger city.

The law presumes the geography of the area is flat without any rivers, roads or mountains to alter a consumer's decision of where to travel to buy goods. It also assumes consumers are indifferent between the actual cities.

The law was developed by William J. Reilly in 1931.

$Ba/Bb= (Pa/Pb)*(Db/Da)square$

A plain English paraphrase would be that the balance or Break Point ($BP$) is equal to the Distance ($d$) between two places, divided by the following: Unity or Total ($1$) plus the Square Root of, the size of Place One ($p_1$) divided by the size of Place Two ($p_2$).

$d$ is distance and $p_1$ and $p_2$ are the sizes of the places between which the distance exists; the answer will give the distance from $p_2$, also called a break-point. What is the break-point? As an example: after leaving a store a you remember something that you wanted to buy; it just so happens that you are headed towards an alternative store b. The break-point can be thought of as the point after which you would travel towards store b instead of store a because of its notional "gravity". This would happen sooner, for example, if store b is an equivalent store but with greater square footage, suggesting that you are more likely to go to store b for greater available utility. This notional gravity can be influenced by a number of things, but square footage is simple and effective.