The retailer's weekly expected profit function is implicitly defined by the demand system in 2.1:
where 
is the retailer's cost
of product i in week t for store s. The complete problem to the
retailer's optimal pricing solution includes pricing, competitor
responses, promotional strategy (eg., feature, display, in-store
couponing, shelf placement, etc.), and costs (eg., forward buying,
inventory control, administrative and selling costs, etc.). We will
concentrate upon pricing, which will yield only a partial solution to
this global problem. A primary reason for concentrating on price is
that it is one of the most important variables under the retailer's
control. A more pragmatic concern is that we have only limited
information about promotional and competitive pressures.
Additionally, we argue that the incremental costs to setting up a
micro-marketing strategy are small. Since we will only consider
changes in prices, these changes should be easy to incorporate into
existing scanner pricing systems.
Dealing with competition is a difficult matter. Price equals marginal cost in a perfectly competitive environment. If a market is perfectly competitive then a consumer will never pay more for a product than the minimum market price. If a store tries to increase the price above this market price then no consumer will purchase its product. On the other extreme if the store is a perfect monopolist, then consumers are unable to buy the same product or service from any other retailer. In our supermarket retailing problem we propose that stores can exercise some local monopoly powers because the store does offer a differentiable service. The store location, product selection, and promotions are not offered in the same way by other competitors.
There are other factors that support the conclusion stores may act as local monopolists: high consumer search and information costs. These high costs are exhibited by their inability to recall store prices outside the store (Dickson and Sawyer 1990, Supermarket Business 1992). Once a consumer enters a store, the incremental cost of engaging in price search of a competitor's non-featured products is quite high compared with the expected gain. Store level research by Kumar and Leone (1988) showed that within-store substitution rates were two to three times greater than substitution across stores induced by promotions in the disposable diaper category. Walters and MacKenzie (1988) suggest that in-store price promotions have little effect on store traffic. Walters (1991) found that store substitution rates were very low compared to brand substitution within a store. This research supports the notion that within store substitution induced by pricing strategies is much higher than across store substitution.
There is also the question of how consumers will react to a retailer carrying out a micro- marketing pricing strategy. Our model assumes that there will be no change in store choice if a retailer chooses a micro-marketing policy. If the prices of items that play an important role in consumers' formulation about price expectations for a store (i.e., loss leaders) are increased, then these changes may have a negative influence on store choice. There may also be circumstances under which consumers may react against different prices in different stores. If a consumer lives on a store's border region and experiences different prices for the same product, that consumer may become angry and switch to a different chain. Since retailers currently have different prices for the same product in different stores, we would not expect strong consumer reactions.
We summarize the previous sub-section by saying that intra-store substitution dominates across- store substitution and competition between stores is occurring through general price levels and promotional strategies. Thus, competition does not naively require every price in the store to be identical with its competitor. If the retailer does not want to induce any change in the current competitive environment, they may still consider price changes that leave their promotional strategy, average price, and total revenues unchanged from their current levels. We do not believe these to be the only viable micro-marketing strategies, but they seem very plausible given the information used in our model.
Essentially this means we will consider changes in everyday
prices
subject to the following two constraints: total sales revenue
and the average price in each store are unchanged from their current
levels. The constraint on sales revenue will guarantee that there is
no change in primary demand. This framework also provides a natural
context for evaluating micro-marketing pricing strategies, since any
profit gains will solely be the result of store-specific pricing
effects and not overall, chain movements.
These constraints can also be supported using economic theory. If the separability of utility across categories within a store is accepted, then implicitly the forms of competition between stores and other retailers must be driven through differences in expenditure levels and average category prices. This follows from the fact that separability implies that category expenditure decisions are only based upon category price indices and not the full vector of prices. (See Section 5 in Deaton and Muellbauer 1980 for an introduction and further references.) Depending upon the form of separability, it may be more proper to constrain category movement instead of category expenditures. Although under indirect weak separability the intra-category budget shares depend only upon total expenditure and group prices, which would support our use of category expenditures as long as other expenditures are constant. Our category price index will be the usual average category price, with each price weighted by its market share.
A consequence of these assumptions is the stability of any new pricing strategy that satisfies these constraints. All pricing strategies that have the same revenue and average price profiles will result in similar competitive environments. Presumably demand and supply are at a stable equilibrium. Thus, any new micro-marketing pricing strategy that leaves revenue and average prices unchanged from their current levels will result in a stable competitive environment. Intuitively this seems reasonable since the current pricing strategy considers not only the refrigerated juice category but also all other categories, promotional strategies, competition, and other intangibles (such as the retailer's experience).
These constraints also have a great deal of intuitive meaning to
retailers. By attempting to keep revenues at a constant level and
assuming the total store expenditures do not change, the retailer is
essentially holding market share constant. Market share is commonly
cited as an objective by retail managers. Alternately if the retailer
elects to use movement market share instead of revenue market share,
we could think of the retailer trying to maintain a certain customer
base. Since most purchases are single units, total movement yields an
indicator for the total number of customers that frequent a category.
The average price constraint can also be thought of as trying to hold
a given level of aggregate consumer utility constant. This implies
that consumers will be indifferent to any price movements within a
category as long as they cancel each other out. An additional reason
from the retailer's standpoint for concentrating on the everyday
component of the pricing problem is that the 75% of profits are made
through the sale of products that are not featured.