The Role of Warehouse Club Membership Fee in Retail Competition
1.Introduction
The core of the warehouse club concept is membership.1 As of this writing, all three major warehouse clubs in the U.S.—Costco, Samrsquo;s Club, and BJrsquo;s—charge members annual membership fees, ranging between $35 and $45. In 2002, 52% of the US households shopped at the retail format, and according to a survey, 30% of shoppers who have not joined a membership warehouse club cite the annual membership fee as the reason.2 Taking their high penetration rate into account, warehouse clubs may now be able to dismiss the complaint by getting rid of the fee policy especially since annual fees account for about 2 percent of their average revenue. Besides, as competition heats up, it has become a big issue whether no-fee format will be a better solution. Despite a 20-year history of warehouse club industry in the U.S., rare attempt has been made to explain the true motivation of the membership policy by warehouse clubs.
In this paper, we build a consumer model of store choice and analyze a duopoly model of competition between a warehouse club and a supermarket. Our results indicate, among others, that the membership fee is related with the supermarketrsquo;s promotional activities. That is, as long as the supermarket has promotions in terms of temporary price reduction, it is optimal for the warehouse club to charge membership fee. Moreover, the deeper the promotion is, the higher is the membership fee. However, the amount of the membership fee is independent of the bulk package size in the warehouse club or the consumerrsquo;s inventory holding cost.
2.The model
2.1Consumer Costs
Suppose a representative consumer consumes q units of the focal product in a given period (e.g., a year). The consumerrsquo;s decisions are (i) whether or not to become a warehouse club member by paying the annual fee (denoted by F ), and as a member, (ii) whether to buy the focal product at the supermarket or at the warehouse club. If the customer is a nonmember, her only store choice is the supermarket. However, some warehouse club members can be opportunistic and shop at a supermarket when the store offers a promotional price for the focal product (i.e., “cherry picking”). In our context, this decision is based on the trade off between the supermarketrsquo;s price (a higher price with occasional promotions) and that of the warehouse club (a lower price but with the membership fee plus extra costs).
For a consumer whose purchase is only from the supermarket, the annual cost of purchasing the focal product is simple. Let denote the retail price at the supermarket and the promotional depth, respectively. We assume the promotional depth is fixed in advance, and the supermarketrsquo;s promotion decision is mainly on its frequency Then her total cost at the supermarket is the average retail price times the quantity:
On the other hand, purchasing at the warehouse club involves two implicit costs in addition to its retail price (denoted by) and the annual fee. The first implicit cost component is the extra travel cost to the warehouse club. Considering relatively easy access to a warehouse club (e.g. via highway), the transportation cost can be better understood as all sorts of inconveniences incurred due to additional shopping trips, such as time cost rather than the distance per se. We assume that consumers are heterogeneous in the extra travel costs per trip (denoted by ), and that these costs are uniformly distributed between 0 and 1.
The second implicit cost component is consumerrsquo;s inventory-holding cost. A typical product in a warehouse club is bulk-packaged (let k denote the bulk size), so that a consumer usually purchases more than what she can consume in one usage instance. The rest of the purchase ( k-1) needs to be stored for future consumption with a constant usage rate. For each unit stored, there is a cost of inventory (denoted by h ) representing the storage space and the opportunity costs. It is straightforward to show that the annual inventory cost becomes
Thus, a consumer who buys the focal product only at the warehouse club spends the total cost of:
represents the total number of extra shopping trips to the warehouse club.
Lastly, when a consumer cherry picks between the two retail formats to pick a lower price at the time of each purchase, she will choose the supermarket with a probability of lambda; and the rest of the time the warehouse club. However, she will still have to pay the annual membership fee to the warehouse club. Thus she incurs a total cost of
The consumer is expected to choose a store by comparing these three purchase costs, from which the demand functions are derived as follows.
2.2Demand and Profit Functions
Based on the assumption that consumers are heterogeneous in their travel costs, we can derive demand functions for the two retailers. In choosing between the two stores, consumers are assumed to have perfect information on the respective prices and on the nature of the supermarket promotion. By comparing the total annual costs of buying the focal product, a consumer chooses among the three shopping choices: warehouse club only, supermarket only, and cherry picking. Consumers with low travel costs ( c ) would find it cheaper to buy only at the warehouse club. Consumers with high travel costs, on the other hand, will find that the lower retail price at the warehouse club cannot justify the extra travel, and they will shop only at the supermarket. However, consumers whose travel costs are in the mid-range will find cherry picking more attractive than patronizing either store. These three consumer segments can be presented in the linear space of the travel cost as in Figure 1.
In the figure, a consumer whose travel cost is would be indiff
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