Retail Pricing with Asymmetric Demand

Recent empirical work suggests that demand functions may, in some cases, be ÒasymmetricÓ. For example, evidence suggests that high quality items ÔstealÕ sales from low quality items, but the converse is not true. It is important to consider the possible impact of such empirical findings of consumer behavior on managerial decision making. In particular, there can be important implications for retail price and promotion decisions. This paper makes an attempt to explore optimal product-line pricing strategies when demand is asymmetric. We first highlight the main considerations using a general demand function for an assortment with two variants. We find, for example, that the optimal price of a variant can decrease when (1) the cost of a higher quality variant decreases, or (2) the cost of a lower quality variant increases. Next, with the help of a specific asymmetric demand formulation, we derive the optimal prices for an assortment with an arbitrary number of variants and develop testable implications. Our empirical analysis, which involves the examination of the pricing strategy of three retailers, supports the implications generated by our mathematical analysis. INTRODUCTION Increasingly, attention is shifting from managing individual products to managing product lines that often vary by quality (e.g., Levy and Weitz 1995, Blattberg and Neslin 1990, Zenor 1994). Given the interactions between products in a line, researchers argue that substantial gains can arise by shifting from ÒproductÓ to Òproduct lineÓ pricing and suggest that a product line manager should replace the popular brand manager (e.g., Zenor 1994). In juxtaposition with this emphasis on product lines, one interesting empirical finding has recently emerged: demand in product lines tends to exhibit some asymmetric patterns (Blattberg and Wisniewski 1989, Blattberg and Neslin 1990). For instance, Blattberg and Wisniewski (1989) report that price reductions by high-quality products moved consumers up in quality 67% of the time, but price reductions by low-quality products moved consumers down only 11 % of the time. As Mulhern and Leone (1991) note: Òwithin retail product lines É substitution patterns are asymmetric -promotions on high price/quality items "steal" sales from low price/quality items, but the converse is not true. This finding has important implications for retail price and promotion decisions because store profitability is affected directly by which brands are selected for price and promotional activity.Ó Behavioral researchers have also devoted some attention to this issue. For example, using metaanalysis and an experiment, Heath and Chatterjee (1995) find support for the presence of such demand patterns and show that the asymmetry can vary across market segments. They note: ÒEvidence É suggests that higher-quality competitors are more resistant to attacks from lowerquality brands than lower-quality competitors are resistant to attacks from higher-quality brands. First, in real-world markets, price discounts move consumers from lower-quality to higher-quality brands more than from higher-quality to lower-quality brands (Bemmaor and Mouchoux 1991; Blattberg and Wisniewski 1989; Kamakura and Russell 1989). Second, loss aversion, the tendency for losses to be more unpleasant than equivalent gains are pleasant, appears to be greater for quality than price. Third, in experimental choice sets, compromise brands draw a larger share from lower-quality than higher-quality brands (Simonson and Tversky 1992).Ó Our primary objective here is to make a first attempt at providing some general guidelines or