A Utility Theory Approach to the Gravity Law: Consumer Shopping Behavior and Trade Areas of Shopping Centers

Abstract

Many papers dealing with shopping behavior and the retail model have been published since Reilly proposed “the Law of Retail Gravitation” in 1931. Among them, Reilly's Law and Huff's Retail Potential Model are especially well-known. These models are of a gravity-type, and are found to be useful in explaining the phenomena of shopping behavior, but since they are empirical they lack theoretical rationale and economic interpretation. In this study the Gravity Law is derived from the utility maximization theory in terms of consumer shopping behavior. This result enables us to interpret the Gravity Law economically.The fundamental hypothesis here is that the individual always seeks to maximize his utility in shopping behavior. The utility is assumed to consist of the number of trips made by the individual to the shopping center and its attractiveness. The utility function is maximized under the time constraint requiring that the total amount of time spent travelling to the shopping center must be equal to or less than the total amount of free time given to the individual. Consequently, the gravity-type model including the number of trips to the shopping center as a subordinate variable can be obtained as a shopping behavioral model. The shopping behavioral model explains that the number of trips to the shopping center is in direct proportion to its attractiveness and in inverse proportion to the travel time. The model structure is similar to that of empirical shopping models which were developed by Reilly and Huff and have been used extensively. As a result, an economic interpretation is able to be given to the gravity model of consumer shopping behavior using the utility maximization theory as a hypothesis.Formulae that are able to estimate the total number of trips to any shopping center and its market share to all of the shopping centers in urban areas, were derived from the gravity-type model obtained above. Similarly, other formulae were obtained for calculating the changes in the total number of trips to the shopping center and its market share to newly proposed shopping complexes. These results are useful for the commercial activity to make a strategy for the development of new shopping centers and for its own allocation planning.The formula to estimate the trade areas of the shopping center was also derived from the shopping behavioral model. The range of trade areas is proportionated to the amount of attractiveness of the shopping center. This result shows that the trade areas proposed by Reilly and Converce are proved theoretically.