Retail Gravity on the Palouse

I have shown how Hotelling's Model explains why retail stores tend to agglomerate in the center. This is, admittedly, a very simplistic explanation.

University of Texas economist William J. Reilly studied the purchases made by the residents of the various counties in Texas. Reilly knew that generally the farther away two counties were from each other the fewer transactions would take place between them. On the other hand if a county had a big city with a lot of bigger retail stores it would act as a magnet attracting the shopping by residents of surrounding and even distant counties. Also a county that had a larger number of residents would have more transactions with a given county than one with a smaller number of residents. Using this data, Reilly published a book in 1931 titled Reilly's Law of Retail Gravitation. In the book, Reilly postulated that two cities of equal size have a trade area boundary midway between the two cities. When cities are of unequal size, the boundary lies closer to the smaller city, giving the larger city a larger trade area.

Reilly's Law calculates a point of indifference (where consumers are indifferent as to which location they use) between two towns in order to determine the retail trade area of each city. Reilly called the boundary between two trade areas the breaking point. On that line, exactly half the population shops at either of the two cities. Obvously, if you were planing on serving both trade areas, you would want to locate as close to this line as possible.

This break point (BP) is equal to the distance (Dab) between the two cities, divided by the following: Unity or total (1) plus the square root of, the population of City A (Pa) divided by the size of City B (Pb). If you have studied physics, you realize this is quite similar to Newton's Law of Gravitation, which states that two bodies attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them

According to the Hotelling Model, the break point should be halfway in between Moscow and Pullman at around 4.65 miles from Pullman. However, since Pullman has a larger population, it is assumed that it will draw more customers. Using the 2005 Census population estimates for Pullman and Moscow and the distance between the center of each city, the break point according to Reilly's Law is 4.8 miles away from Pullman (see chart above). This in part explains why the center of retail gravity on the Palouse is shifted in Moscow's direction. And if Pullman grows more than Moscow, as anticpated, the center will shift even further towards Moscow.


Plotting this out on a map, the theoretical break point between Pullman (A) and Moscow (B) would be approximately at the intersection of SR 270 and Sunshine Road (C). The Hawkins development (D) is two miles to the east of this point.

One of the problems with Reilly's Law is that is not constant for all shopping trips. Retailers can offer additional competitive advantages and this can change the attractiveness of a location. In order to overcome these limitations, several refinements have been made to Reilly's Law. One of these was "Huff's Law of Shopper Attraction." Huff's Law describes retail trade areas on the basis of the size of the store (product assortment), distance, and the sensitivity to travel time associated with the type of product being sought.

The probability of a consumer traveling from home to shopping location A is equal to the square footage of selling space in location A divided by the travel from consumer's home to shopping location A divided by the sum of the square footage of selling space in all different shopping locations (A, B, C...) divided by travel time.

So let's look at the location desirability of Hawkins alone at the SR270/Sunshine Road location versus the desirability of the Hawkins/WarBonnet Plaza/Palouse Mall agglomeration, which was created by land use restrictions in the corridor.

For these calculations, the travel time to the SR270/Sunshine Road location from Pullman is 7 minutes. The travel time to the Hawkins/WarBonnet Plaza/Palouse Mall agglomeration is 11 minutes. Square footage at the SR270/Sunshine Road location is 740,000. Square footage of the Hawkins/WarBonnet Plaza/Palouse Mall agglomeration is roughly 1.32 million.


In this case, even though travel time to the Hawkins/WarBonnet Plaza/Palouse Mall agglomeration is 4 minutes longer, consumers are 6.4% more likely to shop there versus a SR270/Sunshine Road with Hawkins alone.

Hawkins knows all these things already, and that is why they chose the location that they did. It is based on economic science and not any desire to "screw over" Pullman.

Hotelling and Hawkins

In his Town Crier column last Wednesday, Chris Lupke wrote that:

A mall on the Idaho border with no promise of tax revenue won't help our parks or police and won't pave our streets. But what it will do is permanently situate the retail center in and near Moscow, miles from Pullman. Better negotiators could have insisted it be sited closer to our retail base.

Lu Laoshi may be a "national expert" in Chinese and Chinese culture, but he doesn't know jack about the economics of retail.

Some 80 years ago, economist Harold Hotelling devised an analogy to explain the spatial functioning of the marketplace.

His analogy became known as "Hotelling's Model":


Suppose there is a beach which is 100 yards long. Assume beachgoers are spread evenly across the length of the beach. Along come two ice cream vendors. The vendors are selling product of similar quality and price (ceteris paribus.) Logically, the layman would expect the vendors to place their carts at the 25 and 75 yard lines of the beach, thus allowing for an equal division of profits and providing the greatest convenience to beachgoers, as no one would be more than 25 yards from an ice cream cart.

However, one vendor will recognize that by relocating closer to the midpoint of the beach he can achieve an increase in market share. So, on the illustration above, the vendor at Position A will move his cart to the 30 yard line, increasing his market share to 52 1/2 %. The vendor at Position C will compensate by moving his cart to the 70 yard line. This continues as both vendors move incrementally towards the middle of the beach. Eventually, both vendors' carts are at Position B, right next to each other. They have achieved economic equilibrium, with each having a 50% market share.

Hotelling's Model, as you might guess, is very sensitive to cost assumption. There must be some cost to traveling because customers prefer the closest vendor. But these costs must be small, because the people at the end of the beach continue to buy the same amount no matter how far they are from the nearest vendor. If traveling costs are less, then people might not care whether they go to the nearest vendor. If they are greater, so that when the vendor gets far away, people do not bother to go, the vendors will no longer cluster at the middle.

Pullman residents, being six miles away from Hawkins, have negligible traveling costs. Travel costs for Moscow residents are even less. Put the shop in the middle, the customers will come, especially if there is already other retail clustered there. That explains why Hawkins chose the location it did. All very logical and very much in accord with economic principles. That is why the Pullman/Moscow corridor is a potential gold mine.